Results 1 to 10 of about 141 (106)
A theory and methodology to quantify knowledge [PDF]
Royal Society Open Science, 2019 This article proposes quantitative answers to meta-scientific questions including ‘how much knowledge is attained by a research field?’, ‘how rapidly is a field making progress?’, ‘what is the expected reproducibility of a result?’, ‘how much knowledge ...
Daniele Fanelli
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RETRACTED: On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem
Mathematics, 2022 In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an ...
Andrea Ossicini
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Hypercharge quantisation and Fermat's last theorem
SciPost Physics, 2020 What values of the Standard Model hypercharges result in a mathematically consistent quantum field theory? We show that the constraints imposed by the lack of gauge anomalies can be recast as the equation x^3 + y^3 = z^3.
Nakarin Lohitsiri, David Tong
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THEORETICAL ASSUMPTIONS FOR AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY
STED Journal, 2023 Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat's last theorem.
Ognjen Milivojević, Boris Damjanović
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On Two Problems Related to Divisibility Properties of z(n)
Mathematics, 2021 The order of appearance (in the Fibonacci sequence) function z:Z≥1→Z≥1 is an arithmetic function defined for a positive integer n as z(n)=min{k≥1:Fk≡0(modn)}. A topic of great interest is to study the Diophantine properties of this function. In 1992, Sun
Pavel Trojovský
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An elementary proof of Fermat’s last theorem for all even exponents
Journal of Mathematical Cryptology, 2020 An elementary proof that the equation x2n + y2n = z2n can not have any non-zero positive integer solutions when n is an integer ≥ 2 is presented. To prove that the equation has no integer solutions it is first hypothesized that the equation has integer ...
Karmakar Sudhangshu B.
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The Proof of the Fermat’s Conjecture in the Correct Domain
Ratio Mathematica, 2018 The distinction between the Domain of Natural Numbers and the Domain of Line gets highlighted. This division provides the new perception to the Fermat’s Conjecture, where to place it and how to prove it.
Saimir A. Lolja
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Issues in Science and Technology Librarianship, 2013 In May 1995, the major mathematical journal Annals of Mathematics published two articles together proving Fermat's Last Theorem, a mathematical problem that has frustrated mathematicians for over 350 years.
Glenn Masuchika
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International Journal of Mathematics and Mathematical Sciences, 2001 We prove a combinatorial identity which arose from considering the relation rp(x,y,z)=(x+y−z)p−(xp+yp−zp) in connection with Fermat's last theorem.
Joseph Sinyor +2 more
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An Analytical Study of Diophantine Equations of Pythagorean Form: Causal Inferences on Hypothesized Relations between Quadratic and Non-quadratic Triples [PDF]
Athens Journal of EducationIn XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus’ “Arithmetica”, Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x^n+y^n=z^n, have no integer solutions for n>2, and (x,y,z)>0.
Carmelo R. Cartiere
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