Log in

Relevant bibliographies by topics / Proof ;Beal Conjecture: Number theory

Contents

Journal articles
Books
Book chapters
Conference papers

Academic literature on the topic 'Proof ;Beal Conjecture: Number theory'

Author: Grafiati

Published: 5 June 2025

Last updated: 15 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Proof ;Beal Conjecture: Number theory.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Proof ;Beal Conjecture: Number theory"

1

Mohammed, Ghanim. "A SHORT ELEMENTARY PROOF OF THE BEAL CONJECTURE WITH DEDUCTION OF THE FERMAT LAST THEOREM." GLOBAL JOURNAL OF ADVANCED ENGINEERING TECHNOLOGIES AND SCIENCES 8, no. 1 (2021): 1–16. https://doi.org/10.5281/zenodo.4568087.

Full text

Abstract:

The present short paper, which is an amelioration of my previous article “confirmation of the Beal-Brun-Tijdeman-Zagier conjecture” published by the GJETS in 20/11/2019 [15], confirms the Beal’s conjecture, remained open since 1914 and saying that:       The proof uses elementary tools of mathematics, such as the L’Hôpital rule, the Bolzano-Weierstrass theorem, the intermediate value theorem and the growth properties of certain elementary functions. The proof uses also the Catalan-Mihailescu theorem [18] [19] and some methods developed in my paper o

APA, Harvard, Vancouver, ISO, and other styles

2

Earnest, A. G. "Exponents of the class groups of imaginary Abelian number fields." Bulletin of the Australian Mathematical Society 35, no. 2 (1987): 231–46. http://dx.doi.org/10.1017/s0004972700013198.

Full text

Abstract:

It is a classical result, deriving from the Gaussian theory of genera of integral binary quadratic forms, that there exist only finitely many imaginary quadratic fields for which the ideal class group is a group of exponent two. This finiteness has been shown to extend to all those totally imaginary quadratic extensions of any fixed totally real algebraic number field. In this paper we put forward the conjecture that there exist only finitely many imaginary abelian algebraic number fields which have ideal class groups of exponent two, and we examine the extent to which existing methods can be

APA, Harvard, Vancouver, ISO, and other styles

3

Marshall, Stephen M. "An All-Inclusive Proof of Beal’s Conjecture." Bulletin of Society for Mathematical Services and Standards 7 (September 2013): 17–22. http://dx.doi.org/10.18052/www.scipress.com/bsmass.7.17.

Full text

Abstract:

This paper presents a complete and exhaustive proof of the Beal Conjecture. The approach to this proof uses the Fundamental Theorem of Arithmetic as the basis for the proof of the Beal Conjecture. The Fundamental Theorem of Arithmetic states that every number greater than 1 is either prime itself or is unique product of prime numbers. The prime factorization of every number greater than 1 is used throughout every section of the proof of the Beal Conjecture. Without the Fundamental Theorem of Arithmetic, this approach to proving the Beal Conjecture would not be possible.

APA, Harvard, Vancouver, ISO, and other styles

4

Stanojevic, Slobodan. "Beal Conjecture." Bulletin of Society for Mathematical Services and Standards 14 (June 2015): 7–27. http://dx.doi.org/10.18052/www.scipress.com/bsmass.14.7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Huicochea, Mario. "A proof of a conjecture of Lev." International Journal of Number Theory 14, no. 10 (2018): 2583–97. http://dx.doi.org/10.1142/s1793042118501543.

Full text

Abstract:

We say that a set of the form [Formula: see text] for some [Formula: see text] is an interval. For a nonempty finite subset [Formula: see text] of [Formula: see text] and [Formula: see text], Vsevolod Lev proved in [Optimal representations by sumsets and subset sums, J. Number Theory 62(1) (1997) 127–143] some results about the existence of long intervals contained in the [Formula: see text]-fold iterated sumset of [Formula: see text]. Furthermore, in the same paper, he proposed a conjecture [Optimal representations by sumsets and subset sums, J. Number Theory 62(1) (1997) 127–143, Conjecture

APA, Harvard, Vancouver, ISO, and other styles

6

Daw, Christopher, and Jinbo Ren. "Applications of the hyperbolic Ax–Schanuel conjecture." Compositio Mathematica 154, no. 9 (2018): 1843–88. http://dx.doi.org/10.1112/s0010437x1800725x.

Full text

Abstract:

In 2014, Pila and Tsimerman gave a proof of the Ax–Schanuel conjecture for the$j$-function and, with Mok, have recently announced a proof of its generalization to any (pure) Shimura variety. We refer to this generalization as the hyperbolic Ax–Schanuel conjecture. In this article, we show that the hyperbolic Ax–Schanuel conjecture can be used to reduce the Zilber–Pink conjecture for Shimura varieties to a problem of point counting. We further show that this point counting problem can be tackled in a number of cases using the Pila–Wilkie counting theorem and several arithmetic conjectures. Our

APA, Harvard, Vancouver, ISO, and other styles

7

Gica, Alexandru. "The Proof of a Conjecture of Additive Number Theory." Journal of Number Theory 94, no. 1 (2002): 80–89. http://dx.doi.org/10.1006/jnth.2001.2731.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Skutin, Alexander. "Proof of a conjecture of Wiegold." Journal of Algebra 526 (May 2019): 1–5. http://dx.doi.org/10.1016/j.jalgebra.2019.02.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Hart, Bradd. "A proof of morley's conjecture." Journal of Symbolic Logic 54, no. 4 (1989): 1346–58. http://dx.doi.org/10.1017/s0022481200041128.

Full text

Abstract:

In the 1960's, it was conjectured that a complete first order theory in a countable language would have a nondecreasing spectrum on uncountable cardinals. This conjecture became known as Morley's conjecture. Shelah has proved this in [10]. The intent of this paper is to give a different proof which resembles a more naive way of approaching this theorem.Let I(T, λ) = the number of nonisomorphic models of T in cardinality λ. We prove:Theorem 0.1. If T is a complete countable first order theory then for ℵ0 < κ < λ, I(T,K) ≤ I(T, λ).In some sense, one can view Shelah's work on the classifica

APA, Harvard, Vancouver, ISO, and other styles

10

Vong, Seak-Weng, and Xiao-Qing Jin. "Proof of Böttcher and Wenzel's Conjecture." Operators and Matrices, no. 3 (2008): 435–42. http://dx.doi.org/10.7153/oam-02-26.

Full text

APA, Harvard, Vancouver, ISO, and other styles

More sources

Books on the topic "Proof ;Beal Conjecture: Number theory"

1

Wolf. Mathematician's Toolbox: Proof, Logic, and Conjecture. Freeman & Company, W. H., 1998.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

2

Wolf, Robert S. Proof, Logic, and Conjecture: The Mathematician's Toolbox. W. H. Freeman, 1997.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

3

Gaitsgory, Dennis, and Jacob Lurie. Weil's Conjecture for Function Fields. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691182148.001.0001.

Full text

Abstract:

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil's conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of

APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Proof ;Beal Conjecture: Number theory"

1

Mihăilescu, Preda. "A Conditional Proof of the Leopoldt Conjecture for CM Fields." In Transcendence in Algebra, Combinatorics, Geometry and Number Theory. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-84304-5_20.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Ekhad, Shalosh B., and Doron Zeilberger. "Integrals Involving Rudin–Shapiro Polynomials and Sketch of a Proof of Saffari’s Conjecture." 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_15.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Xu, Jin. "Discharging and Structure of Maximal Planar Graphs." In Maximal Planar Graph Theory and the Four-Color Conjecture. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-96-4745-3_2.

Full text

Abstract:

Abstract Recall that the maximal planar graphs are a class of planar graphs with the maximum number of edges, which have been studied extensively since the late 19th century due to the fact that the Four-Color Conjecture can be studied sufficiently for maximal planar graphs. In the subsequent chapters, we will present a series of results related to maximal planar graphs. This chapter mainly discusses the structures of maximal planar graphs by using the proof technique–discharging.

APA, Harvard, Vancouver, ISO, and other styles

4

Mueller, Julia. "A note on Thue’s inequality with few coefficients." In Advances in Number Theory. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198536680.003.0028.

Full text

Abstract:

Abstract A proof of this conjecture or even a weaker version such as the number of primitive solutions of (1.1) depends on r or s is out of reach at the present time. What we are able to prove is the following.

APA, Harvard, Vancouver, ISO, and other styles

5

Lario, Joan-C. "On Serre’s conjecture (3.2.4?) and vertical Weil curves." In Advances in Number Theory. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198536680.003.0021.

Full text

Abstract:

Abstract The first purpose of this contribution is to obtain a general criterion in order to verify this conjecture. In a joint work with P.Bayer [2], we verify (3.2.4?) for the Galois representations defined by the ρ-torsion points of ρ-vertical Weil curves (i.e., modular elliptic curves having bad but potentially good ordinary reduction at ρ, for ρ &gt; 7. Here, we obtain another proof for this case as an application of our general criterion.

APA, Harvard, Vancouver, ISO, and other styles

6

Vojta, Paul. "Arithmetic of Subvarieties of Abelian and Semiabelian Varieties." In Advances in Number Theory. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198536680.003.0016.

Full text

Abstract:

Abstract We will discuss work of Faltings concerning rational points on subvarieties of abelian varieties. In the talk given at the conference, the present author announced a generalization of this theorem to the case of integral points on semiabelian varieties. The proof has some serious flaws, however, so the generalization still remains a conjecture.

APA, Harvard, Vancouver, ISO, and other styles

7

"Matthias Baaz and Pavel Pudlak." In Arithmetic, proof theory, and computational complexity, edited by Peter Clote and Jan KrajÍ ČEk. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198536901.003.0002.

Full text

Abstract:

Abstract The famous conjecture of Kreisel states: If there exists k such that the formal system T prnves φ (Sn(o)) in ≤ k steps for every n, then T proves ∀ x φ (x). Here sn(· ··) denotes n-times iterated successor function. The conjecture was proposed for T = Peano Arithmetic in the formalization of Kleene (cf. [Parikh], [Friedman] problem N.34, [Kreisell]), but it is interesting for any T which contains some fragment of number theory. We shall prove Kreisel’s conjecture for a formal system with finitely many (basic) axioms and the schema of the least number principle for existential formulas L ∃ 1. It should be stressed that the answer to the conjecture depends not so much on the sentences provable in T as it does on the presentation of T and the logical calculus used. For example, it is well known that L ∃ 1 is equivalent to 1 ∑1 [Kaye] and that 1 ∑ 1 is finitely axiomatizable. But our result does not imply anything about I ∑ 1 and it is not implied by the fact that for every sufficiently strong finite axiomatic system Kreisel’s conjecture holds. Thus by writing L ∃ 11 1 ∑ 1 etc. we shall always mean a formal system, not just a deductively closed set of sentences. The reason is that the fact that S and T have the same logical consequences does not imply that we have the same bounds to the number of steps in the proofs. For instance one can prove the following statements:

APA, Harvard, Vancouver, ISO, and other styles

8

Paiva, Carlos Daniel Chaves, Rildo Alves do Nascimento, Isaías José de Lima, et al. "The search for Goldbach's conjecture proof: Exploring your achievements." In Frontiers of Knowledge: Multidisciplinary Approaches in Academic Research. Seven Editora, 2024. http://dx.doi.org/10.56238/sevened2024.026-018.

Full text

Abstract:

Christian Goldbach was a Russian mathematician who lived in the eighteenth century. Although he saw mathematics more as a hobby, he published several works on Number Theory. It is in one of his correspondences with Euler that his conjecture arises, which states that every even number greater than 2 can be expressed as the sum of two prime numbers (equal or not). Despite having a very simple statement, its demonstration requires advanced mathematical knowledge, so much so that to this day it remains without a definitive proof. Obviously, several mathematicians have devoted many years of their lives to the study of Goldbach's conjecture. In this sense, the objective of this research is to list the advances achieved by such mathematicians over time. In addition, we will seek to better understand the historical context in which the conjecture arises. In the end, we will try to highlight the most significant results that at first can be the basis for further research.

APA, Harvard, Vancouver, ISO, and other styles

9

Pickover, Clifford A. "A Ranking of the 10 Most influential Mathematicians Alive Today." In Wonders of Numbers. Oxford University PressNew York, NY, 2001. http://dx.doi.org/10.1093/oso/9780195133424.003.0038.

Full text

Abstract:

Abstract During his 8-year search for a proof, Wiles had brought together most of the breakthroughs in 20th-century number theory and incorporated them in one stupendous proof. Along the way, he created completely new mathematical methods and combined them with traditional ones in novel ways. In doing this, Wiles opened up novel lines of attack on many other mathematical problems and made tremendous contributions toward the resolution of long-standing fundamental problems in number theory. The problems that he has addressed on his own and jointly with others include the Birch and Swinnerton-Dyer conjectures, the main conjecture of Iwasawa theory, and the Shimura-Taniyama-Weil conjecture. Wiles has been awarded the Schock Prize in Mathematics from the Royal Swedish Academy of Sciences and the Prix Fermat from the Universite Paul Sabatier.

APA, Harvard, Vancouver, ISO, and other styles

10

Dunajski, Maciej. "6. Other geometries." In Geometry: A Very Short Introduction. Oxford University Press, 2022. http://dx.doi.org/10.1093/actrade/9780199683680.003.0006.

Full text

Abstract:

‘Other geometries’ offers an overview of some modern geometries and their links with other areas of mathematics, such as Gauss lemma in number theory and Gaussian distributions in statistics. The Atiyah–Singer index theorem, proved in 1963 by Michael Atiyah and Isadore Singer, is a celebrated result of geometry in the last 60 years. Felix Klein had the idea of defining geometry as a pair consisting of a space a two-dimensional plane and a group of all affine transformations of the plane. Grigori Perelman’s proof showed the Poincare conjecture, which was formulated in the early 20th century by French mathematician Henri Poincaré.

APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Proof ;Beal Conjecture: Number theory"

1

Avdyev, Marat Aleksandrovich. "Fermat's Last Theorem and ABC-Conjecture in the School of the XXI Century." In International Scientific and Practical Conference. TSNS Interaktiv Plus, 2024. http://dx.doi.org/10.21661/r-561630.

Full text

Abstract:

In 1637, Pierre de Fermat wrote at the margins of Diophantus’ Arithmetica that he had found a truly wonderful proof of the insolvability of the Diophantine equation a^n + b^n = c^n, where n &gt; 2, but the narrow margins of the books did not allow him to give the full proof. Is there a short and easy way to prove Fermat's Last Theorem? The following ABC conjecture states that for three co-prime numbers A, B, and C which satisfy A + B = C, the product of the prime factors of ABC is usually not much less than C. Both theorems are formulated very simply, but are extremely difficult to prove.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!