Relevant bibliographies by topics / Congruences Modulo

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Congruences Modulo'

Author: Grafiati
Published: 7 June 2025
Last updated: 16 July 2025

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Journal articles on the topic "Congruences Modulo"

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ROSEN, JULIAN. "MULTIPLE HARMONIC SUMS AND WOLSTENHOLME'S THEOREM." International Journal of Number Theory 09, no. 08 (2013): 2033–52. http://dx.doi.org/10.1142/s1793042113500735.

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We give a family of congruences for the binomial coefficient [Formula: see text], with k an integer and p a prime. Our congruences involve multiple harmonic sums, and hold modulo arbitrary large powers of p. The general congruence in our family, which depends on a parameter n, involves n "elementary symmetric" multiple harmonic sums, and holds modulo p2n+3. These congruences are actually part of a much larger collection of congruences for [Formula: see text] in terms of the elementary symmetric multiple harmonic sums. Congruences in our family have been optimized, in that they involve the fewest multiple harmonic sums among those congruences holding modulo the same power of p. The coefficients in our congruences are given by polynomials in k.
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Shen, Erin Y. Y. "Congruences modulo 9 for singular overpartitions." International Journal of Number Theory 13, no. 03 (2017): 717–24. http://dx.doi.org/10.1142/s1793042117500361.

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In a recent work, Andrews introduced the new combinatorial objects called singular overpartitions. He proved that these singular overpartitions can be enumerated by the partition function [Formula: see text] which denotes the number of overpartitions of [Formula: see text] in which no part is divisible by [Formula: see text] and only parts [Formula: see text] may be overlined. In this paper, we consider the function [Formula: see text] from an arithmetical point of view. We establish a number of Ramanujan-like congruences and a congruence relation modulo [Formula: see text] for [Formula: see text] by employing some generating function dissection techniques. With the aid of these congruences and the relation, we obtain two new infinite families of congruences modulo [Formula: see text] satisfied by [Formula: see text].
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RADU, CRISTIAN-SILVIU, and JAMES A. SELLERS. "CONGRUENCES MODULO SQUARES OF PRIMES FOR FU'S k DOTS BRACELET PARTITIONS." International Journal of Number Theory 09, no. 04 (2013): 939–43. http://dx.doi.org/10.1142/s1793042113500073.

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In 2007, Andrews and Paule introduced the family of functions Δk(n) which enumerate the number of broken k-diamond partitions for a fixed positive integer k. In that paper, Andrews and Paule proved that, for all n ≥ 0, Δ1(2n+1) ≡ 0 (mod 3) using a standard generating function argument. Soon after, Shishuo Fu provided a combinatorial proof of this same congruence. Fu also utilized this combinatorial approach to naturally define a generalization of broken k-diamond partitions which he called k dots bracelet partitions. He denoted the number of k dots bracelet partitions of n by 𝔅k(n) and proved various congruence properties for these functions modulo primes and modulo powers of 2. In this note, we extend the set of congruences proven by Fu by proving the following congruences: For all n ≥ 0, [Formula: see text] We also conjecture an infinite family of congruences modulo powers of 7 which are satisfied by the function 𝔅7.
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Garvan, F. G. "More cranks and t-cores." Bulletin of the Australian Mathematical Society 63, no. 3 (2001): 379–91. http://dx.doi.org/10.1017/s0004972700019481.

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Dedicated to George Szekeres on the occasion of his 90th BirthdayIn 1990, new statistics on partitions (called cransk) were found which combinatorially prove Ramanujan's congruences for the partition function modulo 5, 7, 11 and 25. The methods are extended to find cranks for Ramanujan's partition congruence modulo 49. A more explicit form of the crank is given for the modulo 25 congruence.
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Yao, Olivia X. M. "Infinite families of congruences modulo 5 and 7 for the cubic partition function." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 5 (2019): 1189–205. http://dx.doi.org/10.1017/prm.2018.61.

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AbstractIn 2010, Hei-Chi Chan introduced the cubic partition function a(n) in connection with Ramanujan's cubic continued fraction. Chen and Lin, and Ahmed, Baruah and Dastidar proved that a(25n + 22) ≡ 0 (mod 5) for n ⩾ 0. In this paper, we prove several infinite families of congruences modulo 5 and 7 for a(n). Our results generalize the congruence a(25n + 22) ≡ 0 (mod 5) and four congruences modulo 7 for a(n) due to Chen and Lin. Moreover, we present some non-standard congruences modulo 5 for a(n) by using an identity of Newman. For example, we prove that $a((({15\times 17^{3\alpha }+1})/{8})) \equiv 3^{\alpha +1} \ ({\rm mod}\ 5)$ for α ⩾ 0.
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Meštrović, Romeo. "An Extension of a Congruence by Tauraso." ISRN Combinatorics 2013 (December 25, 2013): 1–7. http://dx.doi.org/10.1155/2013/363724.

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For a positive integer let be the th harmonic number. In this paper we prove that, for any prime , . Notice that the first part of this congruence is proposed in 2008 by Tauraso. In our elementary proof of the second part of the above congruence we use certain classical congruences modulo a prime and the square of a prime, some congruences involving harmonic numbers, and a combinatorial identity due to Hernández. Our auxiliary results contain many interesting combinatorial congruences involving harmonic numbers.
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CHAN, HENG HUAT, LIUQUAN WANG, and YIFAN YANG. "CONGRUENCES MODULO 5 AND 7 FOR 4-COLORED GENERALIZED FROBENIUS PARTITIONS." Journal of the Australian Mathematical Society 103, no. 2 (2016): 157–76. http://dx.doi.org/10.1017/s1446788716000616.

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Let $c\unicode[STIX]{x1D719}_{k}(n)$ denote the number of $k$-colored generalized Frobenius partitions of $n$. Recently, new Ramanujan-type congruences associated with $c\unicode[STIX]{x1D719}_{4}(n)$ were discovered. In this article, we discuss two approaches in proving such congruences using the theory of modular forms. Our methods allow us to prove congruences such as $c\unicode[STIX]{x1D719}_{4}(14n+6)\equiv 0\;\text{mod}\;7$ and Seller’s congruence $c\unicode[STIX]{x1D719}_{4}(10n+6)\equiv 0\;\text{mod}\;5$.
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Gouri Shankar Guru. "On Congruences Modulo Powers of 2 for (2, 4)-Regular Overpartitions." Advances in Nonlinear Variational Inequalities 28, no. 7s (2025): 24–36. https://doi.org/10.52783/anvi.v28.4481.

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Recently, Naika et al. (2021) proved several congruence properties modulo powers of 2 for (j,k)-regular overpartition of n for, and . This study establishes several infinite families of congruences modulo powers of 2 for employing q-series identities and iterative computational techniques.
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Yao, Olivia X. M. "Arithmetic properties for Fu's 9 dots bracelet partitions." International Journal of Number Theory 11, no. 04 (2015): 1063–72. http://dx.doi.org/10.1142/s1793042115500566.

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The notion of Fu's k dots bracelet partitions was introduced by Shishuo Fu. For any positive integer k, let 𝔅k(n) denote the number of Fu's k dots bracelet partitions of n. Fu also proved several congruences modulo primes and modulo powers of 2. Recently, Radu and Sellers extended the set of congruences proven by Fu by proving three congruences modulo squares of primes for 𝔅5(n), 𝔅7(n) and 𝔅11(n). More recently, Cui and Gu, and Xia and the author derived a number of congruences modulo powers of 2 for 𝔅5(n). In this paper, we prove four congruences modulo 2 and two congruences modulo 4 for 𝔅9(n) by establishing the generating functions of 𝔅9(An+B) modulo 4 for some values of A and B.
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Jin, Hai-Tao, та Li Zhang. "Ramanujan-type congruences for ℓ-regular partitions modulo 3, 5, 11 and 13". International Journal of Number Theory 13, № 08 (2017): 1995–2006. http://dx.doi.org/10.1142/s179304211750107x.

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Let [Formula: see text] be the number of [Formula: see text]-regular partitions of [Formula: see text]. Recently, Hou et al. established several infinite families of congruences for [Formula: see text] modulo [Formula: see text], where [Formula: see text] and [Formula: see text]. In this paper, using the vanishing property given by Hou et al., we prove an infinite family of congruence for [Formula: see text] modulo [Formula: see text]. Moreover, for [Formula: see text] and [Formula: see text], we obtain three infinite families of congruences for [Formula: see text] modulo [Formula: see text] and [Formula: see text] respectively using the theory of Hecke eigenforms.
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Dissertations / Theses on the topic "Congruences Modulo"

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Hanine, El Mostafa. "Equations diophantiennes p-adiques et congruences modulo p2." Toulouse 3, 1990. http://www.theses.fr/1990TOU30088.

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On demontre que pour tout entier naturel d, il existe un plus petit entier p(d) tel que si p est un nombre premier superieur ou egal a p(d) et f,z#px#1. . . , x#2#d#+#1 sans terme constant de degre d l'equation f(x#1. . . , x#2#d#+#1)0(p#2) admet une solution primitive. On demontre aussi que p(2)=2p(3)=3,p(d)>2 si d4 et p(d)>p si d est multiple de p#2p avec p=2
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Deplagne, Eric. "Système de preuve modulo récurrence." Nancy 1, 2002. http://docnum.univ-lorraine.fr/public/SCD_T_2002_0240_DEPLAGNE.pdf.

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Les méthodes et systèmes de preuve par récurrence sont très diverses. Les méthodes les plus générales sont difficiles à automatiser. Les systèmes automatiques parfois difficiles à justifier. Cette thèse établit au niveau des preuves un lien entre récurrence noethérienne et récurrence par réécriture, ce qui permettra la coopération de systèmes dans un mode sceptique où la preuve est vérifiée grâce à l'isomorphisme de Curry-Howard. Le formalisme de la déduction modulo est étendu au traitement de congruences conditionnelles dont l'évaluation tient compte du contexte. De plus, l'ordre de récurrence qui ne peut pas être compatible avec la congruence, est rendu protecteur, c'est-à-dire qu'il bloque l'application de la congruence. La preuve par récurrence par réécriture est vue comme le résultat de l'internalisation en déduction modulo des hypothèses de récurrence, ce qui permet d'expliquer certains comportements de la méthode de récurrence par réécriture<br>Methods and systems for proof by induction are very different. The most general methods are difficult to automatize. Automated systems are sometimes difficult to justify. This thesis establishes at proof level a link between noetherian induction and induction bt rewriting, which will enable systems to cooperate in a skeptical mode in which the proof is verified thanks to the Curry-Howard isomorphism. The formalism of deduction modulo is extended to conditional congruences which are evaluated with respect to a context. Moreover,the induction ordering, which cannot be compatible with the congruence, is made protective, which means that it blocks the application of the congruence. Proof by induction by rewriting is seen as the result of the internalization of induction hypotheses in deduction modulo, which enables to explain some of the behavior of the induction by rewriting method
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Hakami, Ali Hafiz Mawdah. "Small zeros of quadratic congruences to a prime power modulus." Diss., Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1631.

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Hsu, Catherine. "Higher Congruences Between Modular Forms." Thesis, University of Oregon, 2018. http://hdl.handle.net/1794/23742.

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In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this dissertation, we re-examine Eisenstein congruences, incorporating a notion of “depth of congruence,” in order to understand the local structure of Eisenstein ideals associated to weight 2 cusp forms of squarefree level N. Specifically, we use a commutative algebra result of Berger, Klosin, and Kramer to bound the depth of mod p Eisenstein congruences (from below) by the p-adic valuation of φ(N). We then show how this depth of congruence controls the local principality of the associated Eisenstein ideal.
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Beazer, Miriam. "3-adic Properties of Hecke Traces of Singular Moduli." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/9193.

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As shown by Zagier, singular moduli can be represented by the coefficients of a certain half integer weight modular form. Congruences for singular moduli modulo arbitrary primes have been proved by Ahlgren and Ono, Edixhoven, and Jenkins. Computation suggests that stronger congruences hold for small primes $p \in \{2, 3, 5, 7, 11\}$. Boylan proved stronger congruences hold in the case where $p=2$. We conjecture congruences for singular moduli modulo powers of $p \in \{3, 5, 7, 11\}$. In particular, we study the case where $p=3$ and reduce the conjecture to a congruence for a simpler modular form.
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Hamann, Marco. "Zur Differentialgeometrie zweiparametriger Geradenmengen im KLEINschen Modell." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2005. http://nbn-resolving.de/urn:nbn:de:swb:14-1111593005151-37742.

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In der vorliegenden Arbeit werden Geradenkongruenzen des projektiv abgeschlossenen dreidimensionalen euklidischen Raumes differentialgeometrisch untersucht. Nach J. PLÜCKER lassen sich Geraden in gleicher Weise als Grundelemente eines Geradenraumes auffassen wie die Punkte in einem Punktraum. Unter Beachtung dieser Überlegung scheint eine &amp;quot;natürliche&amp;quot; Behandlung der Geradenkongruenzen interessant und sinnvoll. Sie bildet den Gegenstand der vorliegenden Dissertation. Ein besonderes Augenmerk richtet sich dabei auf die Frage nach &amp;quot;kleinsten&amp;quot; Geradenkongruenzen (&amp;quot;Minimalkongruenzen&amp;quot;) in der Geradenmenge des reellen projektiv abgeschlossenen dreidimensionalen euklidischen Raumes. Dahinter verbirgt sich eine gewisse Analogiebildung in der Liniengeometrie, die der klassischen Differentialgeometrie entstammt. Die Geradenkongruenzen bilden hierbei das liniengeometrische Analogon zu den Flächen des dreidimensionalen (Punkt-)Raumes. Das Wort &amp;quot;Kleinste&amp;quot; stellt im Geradenraum einen Bezug zu den Minimalflächen in der Differentialgeometrie her. Nun gestatten diese Fragestellungen in der Liniengeometrie eine anschauliche Interpretation, sobald man ein Punktmodell des Geradenraumes vorliegen hat. Einparametrige Geradenmannigfaltigkeiten (Regelflächen) lassen sich darin als Kurven und Geradenkongruenzen als zweidimensionale Flächen auffassen. Die vierparametrige Geradenmenge des reellen projektiven dreidimensionalen Raumes ist in diesem Modell eine Quadrik vom Index 2 in einem reellen projektiven fünfdimensionalen Raum, die so genannte KLEINsche Hyperquadrik. Der Modellwechsel wird durch die KLEINsche Abbildung vollzogen<br>In the available work line congruences of the projectively extended three-dimensional euclidean space will be analysed. Following to J. PLÜCKER lines can be seen as basic elements of an line space like in the same way points in a point-space. Taking this fact in consideration a &amp;quot;natural&amp;quot; handling with line congruences might be interesting and reasonable. A special detail in the thesis is the question to minimal congruences in the set of lines of the projectively extended euclidean three-space. It can also be seen as an analogous problem in the geometry of lines which can be find in the differential geometry of surfaces. In this case the line congruences are similar to the surfaces of the three-dimensional (point-)space. The phrase &amp;quot;minimal&amp;quot; means in the line space the connection to the minimal surfaces in the differential geometry. These questions offer in line geometry demonstrative interpretation possibilities if a point-model in the line space exists. One-parameter manifolds of lines (rule surfaces) can be seen in this ambiance as curves and line congruences as two dimensional surfaces. The four-parametric set of lines in the projectively extended three-dimensional euclidian space is in this model a quadric of the index 2 in a real projective five-dimensional space, the so called KLEIN-quadric. The changing of the model is managed by the KLEIN-mapping
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Keck, Ryan Austin. "Congruences for Coefficients of Modular Functions in Levels 3, 5, and 7 with Poles at 0." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8137.

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We give congruences modulo powers of p in {3, 5, 7} for the Fourier coefficients of certain modular functions in level p with poles only at 0, answering a question posed by Andersen and Jenkins and continuing work done by the Jenkins, the author, and Moss. The congruences involve a modulus that depends on the base p expansion of the modular form's order of vanishing at infinity.
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Hamann, Marco. "Zur Differentialgeometrie zweiparametriger Geradenmengen im KLEINschen Modell." Doctoral thesis, [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974391425.

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Moss, Eric Brandon. "Congruences for Fourier Coefficients of Modular Functions of Levels 2 and 4." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6952.

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We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and Jenkins. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also demonstrate congruences for Fourier coefficients of some level 4 modular functions.
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Thornton, David Joshua. "Weakly Holomorphic Modular Forms in Prime Power Levels of Genus Zero." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/6411.

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Let N ∈ {8,9,16,25} and let M#0(N) be the space of level N weakly holomorphic modular functions with poles only at the cusp at infinity. We explicitly construct a canonical basis for M#0(N) indexed by the order of the pole at infinity and show that many of the coefficients of the elements of these bases are divisible by high powers of the prime dividing the level N. Additionally, we show that these basis elements satisfy an interesting duality property. We also give an argument that extends level 1 results on congruences from Griffin to levels 2, 3, 4, 5, 7, 8, 9, 16, and 25.
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Books on the topic "Congruences Modulo"

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Chajda, Ivan. Congruence classes in universal algebra. Heldermann, 2003.

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Freese, Ralph. Commutator theory for congruence modular varieties. Cambridge University Press, 1987.

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Omondi, Amos R. Residue number systems: Theory and implementation. Imperial College Press, 2007.

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Alladi, Krishnaswami, Frank Garvan, and Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. American Mathematical Society, 2014.

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Inc, Common Core. Eureka Math, a Story of Ratios - Grade 8, Module 2: The Concept of Congruence. Wiley & Sons, Incorporated, John, 2013.

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Inc, Common Core. Common Core Mathematics, Grade 10, Module 1: Congruence, Proof, and Constructions. Wiley & Sons, Incorporated, John, 2013.

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Residue Number Systems: Theory and Implementation (Advances in Computer Science and Engineering Texts) (Advances in Computer Science and Engineering Texts). Imperial College Press, 2007.

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Koganzon, Rita. Liberal States, Authoritarian Families. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197568804.001.0001.

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How can liberals justify adult authority over children? Children are born requiring both subordination to adults and education to equip them for citizenship. These requirements are especially vexing for liberal democracies, for whom the exercise of authority is at odds with the natural liberty and equality of citizens. This difficulty has led some liberal theorists to appeal to the liberal state as a model for familial relations and reject parental authority. My book shows that this effort is misguided, and that early liberals understood parental authority as a necessary protection for children’s own future liberty. It was early modern absolutist theorists—Bodin, Filmer, and Hobbes—who sought congruence between the family and the state, arguing that absolute paternal authority was a salutary education for absolutism’s subjects. But early liberals like Locke and Rousseau opposed congruence. Even as they sought to restrict public authority and limit the formal power of parents, they nonetheless sought to strengthen their private authority over children. They saw that undermining traditional authorities would not issue straightforwardly in freedom but would instead elevate the authority of public opinion to new heights and subject citizens to a new tyranny of opinion. To counteract this threat, they buttressed the pedagogical authority of the family to protect children’s future intellectual liberty and defend liberal citizenship. Their educational writings reveal an important corrective insight for modern liberalism: authority is not only not the enemy of liberty, but actually a necessary prerequisite for it.
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Velleman, Leah, and David Beaver. Question-based Models of Information Structure. Edited by Caroline Féry and Shinichiro Ishihara. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199642670.013.29.

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We present approaches to the semantics and pragmatics of information structure which centre on Questions Under Discussion (QUDs). Questions, explicit or implicit, are seen as structuring discourse, and information structural marking is seen as reflecting that underlying discourse structure. Our presentation of the model is largely cast in terms of extensions of Roberts’s (2012b) analysis, which is itself related to Rooth’s (1985/1992) Alternative Semantics and Hamblin’s (1973) approach to the semantics of questions. We present the model in terms of a range of constraints that relate information structure to discourse structure, notably constraints on the ‘Relevance’ of utterances, on the ‘Congruence’ of answers to questions, and on the ‘Availability’ of discourse antecedents. We discuss the application of the approach to the interpretation of focus and some cases of contrastive topics, to discourse structure, to the interpretation of focus sensitive operators, and to certain cases of presupposition projection.
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Williams, Lloyd C. Creating the Congruent Workplace. Praeger, 2002. http://dx.doi.org/10.5040/9798400633300.

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For organizational and personal change to happen and be sustainable, there must first be a system of thought balanced against action. Williams and his concept of congruence provide an alternative to the often chaotic, unbalanced ways in which change is currently understood and its accomplishment attempted. He challenges the organizational model of compartmentalized structures, offers a persuasive refutation of the fashionable paradigm of organizational transformation (one based on dominance and control), and argues a provocative notion that innovation is actually the successful result of reworking what has not worked before. A new look at the processes that create organizational movement, Williams' latest book is a guide for leaders, managers, consultants, and corporate practitioners, and a new way for students, teachers, and researchers to rethink the entire change process. Williams has found through his own experience that people focus too closely on the action behaviors of organizations and too little on the thinking behind them. The result is that gaps open up and create pitfalls in our efforts to achieve excellence in human and organizational performance. Williams suggests that organizations innovate themselves into failure. To counter this, he provides a true systemic approach to enhancing organizational performance, a system of what he visualizes as congruence, a way to fit thoughts to actions. It is as much a way of thinking, says Williams, as it is a method toward goals—goals that are clear and essential to the survival of any organization. Drawing liberally upon his own expertise as a teacher, consultant, and therapist, he helps others to appreciate the successes that can be realized when balance and the alignment of thought and action are achieved, and when the search for change becomes a planned, focused, and systemic endeavor.
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Book chapters on the topic "Congruences Modulo"

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Di Cosmo, Roberto, and Stefano Guerrini. "Strong Normalization of Proof Nets Modulo Structural Congruences." In Rewriting Techniques and Applications. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48685-2_6.

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Garvan, F. G. "Congruences for Andrews’ spt-Function Modulo 32760 and Extension of Atkin’s Hecke-Type Partition Congruences." In Number Theory and Related Fields. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6642-0_8.

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Chan, Hei-Chi, and Shaun Cooper. "Congruences modulo powers of 2 for a certain partition function." In Combinatory Analysis. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7858-4_28.

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Krattenthaler, C. "Congruences Modulo Powers of 2 for the Number of Unique Path Partitions." In Analytic Number Theory, Modular Forms and q-Hypergeometric Series. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68376-8_23.

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Angluin, Dana, Dana Fisman, and Yaara Shoval. "Polynomial Identification of $$\omega $$-Automata." In Tools and Algorithms for the Construction and Analysis of Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45237-7_20.

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Abstract We study identification in the limit using polynomial time and data for models of $$\omega $$-automata. On the negative side we show that non-deterministic $$\omega $$-automata (of types Büchi, coBüchi, Parity or Muller) can not be polynomially learned in the limit. On the positive side we show that the $$\omega $$-language classes $$\mathbb {IB}$$, $$\mathbb {IC}$$, $$\mathbb {IP}$$, and $$\mathbb {IM}$$ that are defined by deterministic Büchi, coBüchi, parity, and Muller acceptors that are isomorphic to their right-congruence automata (that is, the right congruences of languages in these classes are fully informative) are identifiable in the limit using polynomial time and data. We further show that for these classes a characteristic sample can be constructed in polynomial time.
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Childs, Lindsay N. "Congruence Classes Modulo a Polynomial." In A Concrete Introduction to Higher Algebra. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4419-8702-0_28.

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Luttik, Bas, and Nikola Trčka. "Stuttering Congruence for χ." In Model Checking Software. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11537328_16.

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Bachmair, L., I. V. Ramakrishnan, A. Tiwari, and L. Vigneron. "Congruence Closure Modulo Associativity and Commutativity." In Frontiers of Combining Systems. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10720084_16.

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Bachmair, Leo, and Nachum Dershowitz. "Completion for rewriting modulo a congruence." In Rewriting Techniques and Applications. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-17220-3_17.

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Berndt, Bruce C., Chadwick Gugg, and Sun Kim. "Ramanujan’s Elementary Method in Partition Congruences." In Partitions, q-Series, and Modular Forms. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0028-8_2.

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Conference papers on the topic "Congruences Modulo"

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Chubarikov, Vladimir Nikolaevich. "Hua Lo-Ken trees and modular arithmetic with prime power modulo." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-2.

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The report is devoted to the study of polynomial equations in integer p-adic numbers. Criteria are described that reduce the questions of solvability of such equations to questions of solvability of congruences modulo a power of a prime number.
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Das, Kuwali. "Some infinite families of congruences modulo 3 for 7-core partitions." In CETUP* 2015 – WORKSHOP ON DARK MATTER, NEUTRINO PHYSICS AND ASTROPHYSICS AND PPC 2015 – IXTH INTERNATIONAL CONFERENCE ON INTERCONNECTIONS BETWEEN PARTICLE PHYSICS AND COSMOLOGY. Author(s), 2016. http://dx.doi.org/10.1063/1.4954864.

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Lima Neto, Clodomir Silva, Thiago Nascimento da Silva, and Umberto Rivieccio. "Quasi-N4-lattices and their logic." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação, 2022. http://dx.doi.org/10.5753/wbl.2022.222852.

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The variety of quasi-N4-lattices (QN4) was recently introduced as a non-involutive generalization of N4-lattices (algebraic models of Nelson&amp;apos;s paraconsistent logic). While research on these algebras is still at a preliminary stage, we know that QN4 is an arithmetical variety which possesses a ternary as well as a quaternary deductive term, enjoys equationally definable principal congruences and the strong congruence extension property. We furthermore have recently introduced an algebraizable logic having QN4 as its equivalent semantics. In this contribution we report on the results obtained so far on this class of algebras and on its logical counterpart.
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Peña, Cristian Andrey, and Mirela Rigo-Lemini. "Interpretive model of the conceptualization of the congruence of polygons (MICP) / Modelo Interpretativo de la Conceptualización de la Congruencia de Polígonos (MICP)." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-96.

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Shiomi, Daisuke, and Takao Komatsu. "A congruence modulo p of zeta polynomial for cyclotomic function fields." In DIOPHANTINE ANALYSIS AND RELATED FIELDS—2010: DARF—2010. AIP, 2010. http://dx.doi.org/10.1063/1.3478181.

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Chhatre, Kiran, Renan Guarese, Andrii Matviienko, and Christopher Peters. "Evaluating Speech and Video Models for Face-Body Congruence." In I3D '25: Companion Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. ACM, 2025. https://doi.org/10.1145/3722564.3728374.

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Kovačević, Ivana, Jelena Anđelković Labrović, and Milica Jovanović. "Sharing economy value congruence and employees’ workplace satisfaction in co-working spaces." In International Conference on Sharing Economy and Contemporary Business Models: Theory and Practice – “IC-SHARE 2024”. University of Belgrade - Faculty of Organizational Sciences, 2024. http://dx.doi.org/10.62863/qudz9932.

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The sharing economy paradigm inspires changes in various work-related domains by imposing the values of social cohesion, collaborative lifestyle and sustainability. The embodiment of this value system is seen in the evolving trend of co-working space. In order to investigate the relation between the perception of the presence of these specific values in office spatial features and the capacity of the workspace to satisfy the psychosocial needs of occupants, we conducted research on 81 employees working in different office types. It was found that employees recognize availability, collaboration, ability to create networks and openness, as more represented values and satisfaction with personalisation and territoriality more linked with them Results also show that there is a correlation between perceived values and workspace satisfaction with the focus on the needs for status congruency that becomes more emphasized in traditional shared offices along with the identification needs, which becomes the challenge for modern co-working offices.
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Rocha, Maria Célia Furtado, and Sara Raskin. "Seleção de Ferramenta CASE para o Estado da Bahia – Um caso de uso da NBR ISO/IEC 14102/1999." In Simpósio Brasileiro de Qualidade de Software. Sociedade Brasileira de Computação - SBC, 2002. http://dx.doi.org/10.5753/sbqs.2002.16225.

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O presente artigo pretende analisar o processo de avaliação e seleção de ferramenta CASE para o Estado da Bahia, com o objetivo de identificar pontos relevantes da experiência e verificar as condições mais prováveis para a ocorrência de aplicações da NBR ISO/IEC 14102/1999 congruentes com as práticas preconizadas pelo novo modelo de gerenciamento.
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Tew, Neal, Priyank Kalla, Namrata Shekhar, and Sivaram Gopalakrishnan. "Verification of arithmetic datapaths using polynomial function models and congruence solving." In 2008 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, 2008. http://dx.doi.org/10.1109/iccad.2008.4681562.

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Yu, Hongrong, and James J. S. Stone. "Viscoelastic Finite Element Contact Analysis of Articular Joints." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0108.

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Abstract Joint contact analysis of the musculoskeletal system is one of the important biomechanical research topics due to its significant clinical relevance. The articular cartilage and its mechanical behavior play a key role in the articular joint contact. Articular joint models considering the time-dependent viscoelastic properties of cartilage, and joint congruences were studied. Results of the maximum normal contact stresses and related contact region versus time for two-dimensional plane stress and three-dimensional axisymmetric cases are presented.
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Reports on the topic "Congruences Modulo"

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Ingram, Keisha LaRaine, Dorsa Dorbahani, Anzhela Sargsyan, and Mannhas Kamble. Promotion of Luxurious Cosmetics Through Emotion Manipulation. Vilnius Business College, 2024. https://doi.org/10.57005/ab.2024.3.2.

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Considering the rising importance of emotions in influencing the purchase decisions of consumers, this research highlights emotions and the ways in which they impact the purchase behaviour. This is significant regarding information the marketers use to develop the strategies and practices for targeting consumer emotions, which ineffectively influence their purchase decisions for luxury cosmetics products. Indeed, this a challenge that marketers have faced in correctly aligning their marketing mix strategies to connect with these consumer groups. Conventional marketing strategies used to capture emotion as a factor to determine consumer choices have historically enable commercial success for luxury brands, however, this research explores emotions and moods using the Mood Congruency Model and Affect-as-Information Model to determine consumer purchase behaviour for luxury cosmetics products.
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Castro Salgado, José William, and Liliana Santamaria Ariza. Evaluación del proyecto institucional: un diagnóstico para su comprensión y mejora. Universidad Militar Nueva Granada, 2024. http://dx.doi.org/10.18359/docinst.7536.

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La elaboración de diagnósticos se posiciona como una herramienta fundamental en el desarrollo de proyectos, al ofrecer una visión integral de las fortalezas y debilidades de una institución. Este proceso no solo permite la identificación de aspectos críticos, sino que también establece una línea base esencial para la formulación de objetivos concretos y la definición de estrategias que guíen el accionar institucional. En este contexto, los diagnósticos participativos han adquirido una relevancia creciente, al proporcionar una perspectiva directa de los beneficiarios, usuarios o clientes, permitiendo así identificar sus necesidades, expectativas y oportunidades con respecto a los productos o servicios ofrecidos. Por ende, su diseño debe integrar variables que faciliten el reconocimiento e intercambio de experiencias, promoviendo la inclusión de la diversidad y la pluralidad de los participantes. En el contexto de la Universidad Militar Nueva Granada (UMNG), los diagnósticos se establecen como una herramienta esencial para evaluar el progreso en diversas áreas misionales en relación con la estrategia institucional. En este sentido, resulta crucial llevar a cabo una evaluación del Proyecto Institucional (PI) que permita medir la pertinencia, el impacto, la congruencia y el grado de alineación con otros documentos maestros. Con este propósito, se ha desarrollado el presente diagnóstico, el cual integra una variedad de herramientas destinadas a abordar el análisis documental, la evaluación de capacidades, la apuesta competitiva y la posterior sistematización de la información. Mediante este análisis, se busca determinar la eficiencia y consistencia del modelo de negocio como respuesta a las cambiantes demandas y necesidades del entorno institucional.
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