Relevant bibliographies by topics / Fermat numbers

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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 'Fermat numbers'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Fermat numbers"

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Annouk, Ikorong. "A Note on Numbers." European Journal of Applied Science, Engineering and Technology 2, no. 2 (2024): 330–33. http://dx.doi.org/10.59324/ejaset.2024.2(2).24.

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A Fermat number is a number of the form F_n=2^(2^n )+1, where n is an integer ≥ 0. A Fermat composite (see [1] or [2] or [4]) is a non prime Fermat number and a Fermat prime is a prime Fermat number. Fermat composites and Fermat primes are characterized via divisibility in [4] and in [5]. It is known (see [4]) that for every j ∈ {0, 1, 2, 3, 4}, Fj is a Fermat prime and it is also known (see [2] or [3]) that F5 and F6 are Fermat composites. In this paper, we show [via elementary arithmetic congruences] the following result (E.). For every integer n > 0 such that n ≡ 1 mod [2], we have Fn-1
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Annouk, Ikorong. "A Note on Numbers." European Journal of Applied Science, Engineering and Technology 2, no. 2 (2024): 330–33. https://doi.org/10.59324/ejaset.2024.2(2).24.

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A Fermat number is a number of the form F_n=2^(2^n )+1, where n is an integer ≥ 0. A Fermat composite (see [1] or [2] or [4]) is a non prime Fermat number and a Fermat prime is a prime Fermat number. Fermat composites and Fermat primes are characterized via divisibility in [4] and in [5]. It is known (see [4]) that for every j ∈ {0, 1, 2, 3, 4}, Fj is a Fermat prime and it is also known (see [2] or [3]) that F5 and F6 are Fermat composites. In this paper, we show [via elementary arithmetic congruences] the following result (E.). For every integer n > 0 such that n ≡ 1 mod [2],
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Madhavan, C. E. Veni. "Factoring fermat numbers." Resonance 1, no. 1 (1996): 108. http://dx.doi.org/10.1007/bf02838870.

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KULOĞLU, BAHAR. "GAUSSIAN FERMAT NUMBERS, POLYNOMIALS AND THEIR ASSOCIATED TRANSFORMS." Journal of Science and Arts 24, no. 3 (2024): 573–90. http://dx.doi.org/10.46939/j.sci.arts-24.3-a11.

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In this paper, we introduced Gaussian Fermat numbers and polynomials. We provided the Binet formula, generating functions, and the exponential generating function for these numbers and polynomials. Additionally, we derived several identities for these polynomials, including the Cassini identity, Catalan identity, Vajda identity, Halton identity, Gelin-Cesaro identity, and D’Ocagne’s identity. We demonstrated that Gaussian Fermat numbers and polynomials can also be obtained through matrix representations and discussed key propositions based on the fact that the determinants of these matrix repr
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Kalashnіkova, N. V. "Some properties of prime numbers of special form and Carmichael numbers." Researches in Mathematics 24 (September 1, 2016): 41. http://dx.doi.org/10.15421/241607.

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We study some properties of structure of the multiplicative group $Z^*_m$, in case when m is Mersenne prime, Fermat or Carmichael number. Using the results of these studies, we obtain properties of Mersenne primes, Fermat and Carmichael numbers.
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Annouk, Ikorong, and Paul Archambault. "A Short Note on Numbers of the Form K + Fn, Where K ? {2, 4, 8} and Fn is a Fermat Number." Sumerianz Journal of Scientific Research, no. 53 (August 26, 2022): 60–62. http://dx.doi.org/10.47752/sjsr.53.60.62.

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A Fermat number is a number of the form , where n is an integer 0. A Fermat composite (see Dickson [1] or Hardy and Wright [2] or Ikorong [3]) is a non-prime Fermat number and a Fermat prime is a prime Fermat number. Fermat composites and Fermat primes are char­acterized via divisibility in Ikorong [3] and in Ikorong [4]. It is known (see Ikorong [3]) that for every j ∈ {0, 1, 2, 3, 4}, Fj is a Fermat prime and it is also known (see Hardy and Wright [2] or Paul [5]) that F5 and F6 are Fermat composites 641×6700417, and since 2013, it is known that +1 is Fermat composite number). In this paper,
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Vavilov, Nikolai. "Computers as Novel Mathematical Reality. VI. Fermat numbers and their relatives." Computer tools in education, no. 4 (December 28, 2022): 5–68. http://dx.doi.org/10.32603/2071-2340-2022-4-5-67.

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In this part, which constitutes a pendent to the part dedicated to Mersenne numbers, I continue to discuss the fantastic contributions towards the solution o classical problems of number theory achieved over the last decades with the use of computers. Specifically, I address primality testing, factorisations and the search of prime divisors of the numbers of certain special form, primarily Fermat numbers, their friends and relations, such as generalised Fermat numbers, Proth numbers, and the like. Furthermore, we discuss the role of Fermat primes and Pierpoint primes in cyclotomy.
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Ipek, Ahmet. "On Some Recurrence Relations Connected with Generalized Fermat Numbers and Some Properties of Divisibility for these Numbers." Asian Journal of Advanced Research and Reports 18, no. 5 (2024): 38–42. http://dx.doi.org/10.9734/ajarr/2024/v18i5630.

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As a result of nice properties of Fermat numbers and their interesting applications, these numbers have recently seen a variety of developments and extensions. Within this framework, this paper contributes. The purpose of this paper is to obtain some recurrence relations connected with generalized Fermat numbers \(\mathcal{F}\)\(\mathcal{n}\) = \(\mathcal{a}\)2\(\mathcal{n}\) + 1 for \(\mathcal{a}\); \(\mathcal{n}\) \(\epsilon\) \(\mathbb{Z}\) and \(\mathcal{n}\) \(\geq\) 0 and as a result of these recurrent relations, to get some properties of divisibility for generalized Fermat numbers.
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Tang, Min, and Jian-Xin Weng. "JEŚMANOWICZ' CONJECTURE WITH FERMAT NUMBERS." Taiwanese Journal of Mathematics 18, no. 3 (2014): 925–30. http://dx.doi.org/10.11650/tjm.18.2014.3942.

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Gostin, Gary B. "New factors of Fermat numbers." Mathematics of Computation 64, no. 209 (1995): 393. http://dx.doi.org/10.1090/s0025-5718-1995-1265015-9.

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Dissertations / Theses on the topic "Fermat numbers"

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Mižutavičiūtė, Asta. "Pirminių skaičių generavimas Mažosios Ferma teoremos metodu." Bachelor's thesis, Lithuanian Academic Libraries Network (LABT), 2013. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2013~D_20130129_145153-50255.

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Šiame darbe matematine sistema MathCAD sukūrėme programą dideliems pirminiams skaičiams rasti. Išanalizavome pirminių, netikrų pirminių ir pseudopirminių skaičių pasiskirstymą.<br>In this thesis by mathematical system MathCAD we created the program for finding large prime numbers. Also, we analysed distribution of unreal prime, pseudoprime and prime numbers.
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Santos, João Evangelista Cabral dos. "Números inteiros como soma de quadrados." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7546.

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Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-04T11:39:40Z No. of bitstreams: 2 arquivototal.pdf: 1037710 bytes, checksum: 4e3c7e69a8c60214c05fdcac3db1ec5e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-04T11:41:46Z (GMT) No. of bitstreams: 2 arquivototal.pdf: 1037710 bytes, checksum: 4e3c7e69a8c60214c05fdcac3db1ec5e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Made available in DSpace on 2
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Ferreira, Antônio Eudes. "Números primos e o Postulado de Bertrand." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/9336.

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-29T15:44:42Z No. of bitstreams: 1 arquivototal.pdf: 691607 bytes, checksum: 68ddd45857d5c0c6e60229a957089adf (MD5)<br>Approved for entry into archive by Fernando Souza (fernandoafsou@gmail.com) on 2017-08-29T15:47:36Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 691607 bytes, checksum: 68ddd45857d5c0c6e60229a957089adf (MD5)<br>Made available in DSpace on 2017-08-29T15:47:36Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 691607 bytes, checksum: 68ddd45857d5c0c6e60229a957089adf (MD5) Previous issue date: 2014-08-01<br>
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Saucedo, Antonio Jr. "Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/855.

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Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.
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Alkauskas, Giedrius. "Several problems from number theory." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20091008_155751-23469.

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Doctoral thesis is devoted to investigation of three problems. The first one deals with the analytic properties and representation in closed or almost closed form of the Stieltjes tranform of the Minkowski question mark function (that is, the generating function of moments, the so called dyadic period function). The main result claims that the dyadic period function can be represented as a convergent series of rational functions with rational coefficients. In the proof the techniques from complex dynamics, analytic theory of continued fractions, the theory of several complex variables are bein
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Deconinck, Heline. "The generalized Fermat equation over totally real number fields." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/81893/.

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Levitt, Benjamin L. "Tate-Shafarevich Groups of Jacobians of Fermat Curves." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/193812.

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For a fixed rational prime p and primitive p-th root of unity ζ, we consider the Jacobian, J, of the complete non-singular curve give by equation yᵖ = xᵃ(1 − x)ᵇ. These curves are quotients of the p-th Fermat curve, given by equation xᵖ+yᵖ = 1, by a cyclic group of automorphisms. Let k = Q(ζ) and k(S) be the maximal extension of k unramified away from p inside a fixed algebraic closure of k. We produce a formula for the image of certain coboundary maps in group cohomology given in terms of Massey products, applicable in a general setting. Under specific circumstance, stated precisely below, we
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Benaissa, Mohammed. "VLSI algorithms, architectures and design for the Fermat Number Transform." Thesis, University of Newcastle Upon Tyne, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.254020.

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Pajayakrit, A. "VLSI architecture and design for the Fermat Number Transform implementation." Thesis, University of Newcastle Upon Tyne, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379767.

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Clark, John. "On a conjecture involving Fermat's Little Theorem." [Tampa, Fla] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002485.

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Books on the topic "Fermat numbers"

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Brudner, Harvey J. Fermat and the missing numbers. WLC, Inc., 1994.

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Křížek, Michal, Florian Luca, and Lawrence Somer. 17 Lectures on Fermat Numbers. Springer New York, 2001. http://dx.doi.org/10.1007/978-0-387-21850-2.

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Bussotti, Paolo. Sulle orme di Fermat: Il teorema dei numeri poligonali e la sua dimostrazione. Agorà Publishing, 2009.

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Florian, Luca, and Somer Lawrence, eds. 17 lectures on Fermat numbers: From number theory to geometry. Springer, 2001.

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Cox, David A. Primes of the form p = x² + ny²: Fermat, class field theory, and complex multiplication. John Wiley & Sons, Inc., 2013.

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Singh, Simon. L'ultimo teorema di Fermat. Rizzoli, 1999.

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Singh, Simon. El enigma de Fermat. Planeta, 2004.

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Bussotti, Paolo. From Fermat to Gauss: Indefinite descent and methods of reduction in number theory. Dr. Erwin Rauner Verlag, 2006.

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Edwards, Harold M. Fermat's last theorem: A genetic introduction to algebraic number theory. 5th ed. Springer, 1996.

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Orme, Tall David, ed. Algebraic number theory. 2nd ed. Chapman and Hall, 1987.

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Book chapters on the topic "Fermat numbers"

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Rassias, Michael Th. "Perfect numbers, Fermat numbers." In Problem-Solving and Selected Topics in Number Theory. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-0495-9_3.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "Generalizations of Fermat Numbers." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_13.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "Primality of Fermat Numbers." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_5.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "Divisibility of Fermat Numbers." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_6.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "Factors of Fermat Numbers." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_7.

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Harborth, Heiko. "Fermat-Like Binomial Equations." In Applications of Fibonacci Numbers. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-015-7801-1_1.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "Basic Properties of Fermat Numbers." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_3.

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Poulo, Richard. "Fermat and His Last Theorem." In Mathematicians Don't Work With Numbers. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58916-4_33.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "Introduction." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_1.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "The Irrationality of the Sum of Some Reciprocals." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_10.

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Conference papers on the topic "Fermat numbers"

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Liu, Jingpeng, Sheng Cui, Ming Tang, et al. "Nyquist Filtering Based on Fermat Number Transform." In Optical Fiber Communication Conference. Optica Publishing Group, 2025. https://doi.org/10.1364/ofc.2025.th2a.8.

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The Fermat number transform is innovatively applied to Nyquist filtering, reducing hardware complexity by ~80% when the ROF=0.01, while maintaining equivalent performance compared with conventional frequency- and time- domain Nyquist filters.
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Goswami, Partha Sarathi, Tamal Chakraborty, and Abir Chattopadhyay. "A Secured Quantum Key Exchange Algorithm using Fermat Numbers and DNA Encoding." In 2021 Fourth International Conference on Electrical, Computer and Communication Technologies (ICECCT). IEEE, 2021. http://dx.doi.org/10.1109/icecct52121.2021.9616749.

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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.

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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 &amp;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.
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Al-Gailani, M. F., S. Boussakta, and J. Neasham. "Fermat Number Transform diffusion's analysis." In 2011 IEEE GCC Conference and Exhibition (GCC). IEEE, 2011. http://dx.doi.org/10.1109/ieeegcc.2011.5752501.

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Kim, Nam-Ho, and Samuel M. Song. "Motion estimation by Fermat number transform." In Photonics West 2001 - Electronic Imaging, edited by Bernd Girod, Charles A. Bouman, and Eckehard G. Steinbach. SPIE, 2000. http://dx.doi.org/10.1117/12.411856.

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Reed, I. S., T. K. Truong, J. J. Chang, H. M. Shao, and I. S. Hsu. "VLSI residue multiplier modulo a Fermat number." In 1985 IEEE 7th Symposium on Computer Arithmetic (ARITH). IEEE, 1985. http://dx.doi.org/10.1109/arith.1985.6158948.

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Varuna Rao, K. M., and Umesh Ghanekar. "Transform domain fragile watermarking using fermat number transform." In 2015 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC). IEEE, 2015. http://dx.doi.org/10.1109/iccic.2015.7435691.

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Xu, Weihong, Xiaohu You, and Chuan Zhang. "Using Fermat number transform to accelerate convolutional neural network." In 2017 IEEE 12th International Conference on ASIC (ASICON). IEEE, 2017. http://dx.doi.org/10.1109/asicon.2017.8252655.

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Al-Aali, Yousuf, and Said Boussakta. "Lightweight Hash Function based on Fermat Number Transform (FNT)." In 2023 International Conference on Computer, Information and Telecommunication Systems (CITS). IEEE, 2023. http://dx.doi.org/10.1109/cits58301.2023.10188697.

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Baozhou, Zhu, Nauman Ahmed, Johan Peltenburg, Koen Bertels, and Zaid Al-Ars. "Diminished-1 Fermat Number Transform for Integer Convolutional Neural Networks." In 2019 IEEE 4th International Conference on Big Data Analytics (ICBDA). IEEE, 2019. http://dx.doi.org/10.1109/icbda.2019.8713250.

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Reports on the topic "Fermat numbers"

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Pengelley, David. Figurate Numbers and Sums of Numerical Powers: Fermat, Pascal, Bernoulli. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci003987.

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Anderson, Sharron, Antony Lloyd, Malcom Baxter, Michael Walls, and Victoria Bailey-Horne. Turmeric survey – Final report. Food Standards Agency, 2022. http://dx.doi.org/10.46756/sci.fsa.ojv940.

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The consumption of turmeric supplements is increasingly popular and is reported to provide numerous health benefits including antioxidant, analgesic, anti-inflammatory, antiseptic, anticarcinogenic, chemopreventive, chemotherapeutic, antiviral, antibacterial, antifungal and antiplatelet activities [1]. However, in recent months there has been a number of reports of hepatotoxicity linked to the consumption of these supplements. Such reports and scientific publications led to a review of the safety of turmeric and curcumin by the UK Committee on Toxicity of Chemicals in Food, Consumer Products a
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