Results 41 to 50 of about 81,722 (194)
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
The quartic Fermat equation in Hilbert class fields of imaginary quadratic fields
, 2015 It is shown that the quartic Fermat equation x4 + y4 = 1 has nontrivial integral solutions in the Hilbert class field Σ of any quadratic field whose discriminant satisfies -d ≡ 1 (mod 8). A corollary is that the quartic Fermat equation has no nontrivial
Rodney Lynch +3 more
core +1 more source
A Quartic Identity Related to Fermat-Type Equations
, 2014 6 ...
Winkler, Mike, Fillipi, Andreas
openaire +2 more sources
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
wiley +1 more source
Fermat type differential and difference equations
Electronic Journal of Differential Equations, 2015 Summary: This article we explore the relationship between the number of differential and difference operators with the existence of meromorphic solutions of Fermat type differential and difference equations. Some Fermat differential and difference equations of certain types are also considered.
Kai Liu, Xianjing Dong
openaire +2 more sources
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
f$f$‐Diophantine sets over finite fields via quasi‐random hypergraphs from multivariate polynomials
Mathematika, Volume 72, Issue 2, April 2026.Abstract We investigate f$f$‐Diophantine sets over finite fields via new explicit constructions of families of quasi‐random hypergraphs from multivariate polynomials. In particular, our construction not only offers a systematic method for constructing quasi‐random hypergraphs but also provides a unified framework for studying various hypergraphs ...
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
wiley +1 more source
Zagier’s reduction theory for indefinite binary quadratic forms and the Fermat-Pell Equation [PDF]
, 2020 We give an in depth description of indefinite binary quadratic forms with a particular emphasis on Zagier’s reduction theory for such forms. We also connect this theory with the theory of minus continued fractions and as a further application we offer a ...
Steward, Stephen Michael +1 more
core
Fermat's type equations in the set of 2×2 integral matrices
Tsukuba Journal of Mathematics, 1998 Let \((*)\) be \(X^n+ Y^n= Z^n\) and \((**)\) be \(X^n+ Y^n+ Z^n= W^n\) \((n\geq 1)\). Let \(G(k,m)= \{M\); \(\text{det}(M)= m\}\), where \(M= \left( \begin{smallmatrix} r&b\\ ks&r \end{smallmatrix} \right)\), \(r,s\in \mathbb{Z}\); \(k\) a fixed positive integer not a perfect square. The following theorems are proved: 1.
Cao, Zhenfu, Grytczuk, Aleksander
openaire +2 more sources