Results 11 to 20 of about 892 (168)

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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Extending the plane trigonometric proof of Fermat's Last Theorem to the case n=3 [PDF]

Notes on Number Theory and Discrete Mathematics
We extend the plane trigonometric approach that we used to prove the case n=4 of Fermat's Last Theorem, to the case n=3. We show that all real positive triplets satisfying a^ϕ+b^ϕ=cϕ for ϕ>1 are triangles. As in the case of n=4, we equate the Pythagorean
Giri Prabhakar
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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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Hurray for Fermat and Wiles!: A Bibliographic Essay on the Modern Literature Pertaining to Arguably the World's Most Famous Unsolved (until May 1995) Mathematical Theorem.

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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A new combinatorial identity

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, Ted Speevak, Akalu Tefera   +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 Education
In 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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Fermat’s last theorem and chaoticity [PDF]

Natural Computing, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

On a few Diophantine equations, in particular, Fermat's last theorem

International Journal of Mathematics and Mathematical Sciences, 2003
This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems.
C. Levesque
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