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International Journal of Mathematics and Mathematical Sciences, 1986 It is shown how to find all integers a, b such that a + b, a2 + b2 and a3 + b3 are simultaneously perfect squares.
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Basic Diophantine Relations [PDF]
Formalized Mathematics, 2018 Summary The main purpose of formalization is to prove that two equations y a ( z )= y , y = xz are Diophantine ...
Marcin Acewicz, Karol Pak
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IEEE AccessIn multi-criteria decision-making (MCDM) situations, it is widely noticed that the resolution method is impacted by the existence of imprecise information and uncertainty in the decision maker’s assessment.
Muhammad Umar Mirza +4 more
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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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On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
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Fourier Expansion‐Based Approach to the Parameter Space of Classical Systems
Annalen der Physik, Volume 538, Issue 7, July 2026.ABSTRACT We propose a new approach to compute the classical metric tensor (CMT) and the Hannay curvature using Fourier series expansions in action‐angle variables. This approach circumvents the need for complex time‐domain integrals or the construction of generating functions, replacing them with algebraic combinations of Fourier coefficients. We prove
Marcos J. Hernández +3 more
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Diophantine Approximation and Coloring [PDF]
The American Mathematical Monthly, 2015 16 pages, pre-publication version of paper which will appear in American Mathematical ...
Alan Haynes, Sara Munday
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Diophantine equations involving factorials [PDF]
, 2017 summary:We study the Diophantine equations $(k!)^n -k^n = (n!)^k-n^k$ and $(k!)^n +k^n = (n!)^k +n^k,$ where $k$ and $n$ are positive integers. We show that the first one holds if and only if $k=n$ or $(k,n)=(1,2),(2,1)$ and that the second one holds if ...
Luca, Florian, Alzer, Horst
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Teaching Congruences in Connection with Diophantine Equations
Education Sciences, 2021 The presented paper is devoted to the new teaching model of congruences of computer science students within the subject of discrete mathematics at universities.
Ďuriš Viliam +3 more
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Energy Science &Engineering, Volume 14, Issue 7, Page 3250-3271, July 2026.This study introduces bipolar q‐fractional fuzzy sets and new aggregation operators to support renewable energy selection under uncertainty. The proposed decision‐making framework effectively integrates positive and negative evaluations, ensuring consistent ranking and robust performance, as demonstrated through practical analysis and comparative ...
Sagvan Y. Musa +3 more
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