Results 51 to 60 of about 651 (161)
, 2022 A simpler proof of Fermat Last Theorem (FLT), formulated by Fermat in 1637, is suggested. The initial equation x^n + y^n = z^n is considered not in natural, but in integer numbers.
Shestopaloff, Yuri K.
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
wiley +1 more source
Generalized Fermat equations: A miscellany
, 2015 This paper is devoted to the generalized Fermat equation xp + yq = zr, where p, q and r are integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent triples (p, q, r), including a number of infinite families, for which ...
Dahmen, S.R.; id_orcid +4 more
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, 2022 A simpler proof of Fermat Last Theorem (FLT), formulated by Fermat in 1637, is suggested. The initial equation x^n + y^n = z^n is considered not in natural, but in integer numbers.
Shestopaloff, Yuri K.
core +1 more source
Solving the n $n$‐Player Tullock Contest
Journal of Public Economic Theory, Volume 28, Issue 2, April 2026.ABSTRACT The n $n$‐player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can the model be solved more generally?
Christian Ewerhart
wiley +1 more source
Hypergraphs with arbitrarily small codegree Turán density
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract The codegree Turán density γ(F)$\gamma (F)$ of a k$k$‐graph F$F$ is the smallest γ∈[0,1)$\gamma \in [0,1)$ such that every k$k$‐graph H$H$ with δk−1(H)⩾(γ+o(1))|V(H)|$\delta _{k-1}(H)\geqslant (\gamma +o(1))\vert V(H)\vert$ contains a copy of F$F$. In this work, we show that for every ε>0$\varepsilon >0$, there is a k$k$‐uniform hypergraph F$F$
Simón Piga, Bjarne Schülke
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$S$-unit equations and the asymptotic Fermat conjecture over number fields
, 2022 Recent attempts at studying the Fermat equation over number fields haveuncovered an unexpected and powerful connection with $S$-unit equations. Inthis expository paper we explain this connection and its implications for theasymptotic Fermat conjecture.
Ozman, E. ; https://orcid.org/ +1 more
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Distribution of integer points on determinant surfaces and a mod‐p analogue
Mathematika, Volume 72, Issue 2, April 2026.Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
wiley +1 more source
Elementary proof of Fermat Last Theorem based on parity considerations and binomial expansions
, 2019 An elementary proof of Fermat Last Theorem (FLT) on the basis of binomial expansions and parity considerations is proposed. FLT was formulated by Fermat in 1637, and proved by A. Wiles in 1995. Here, a simpler approach is studied.
Shestopaloff Yu. K.
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A common approach to three open problems in number theory [PDF]
Discrete Mathematics Letters, 2023 Apoloniusz Tyszka
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