Results 51 to 60 of about 1,224,172 (204)

Three Diophantine equations concerning the polygonal numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Many authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPₖ(x)+nPₖ(y)=z², where Pₖ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
doaj   +1 more source

The Benjamin–Ono Equation in the Zero‐Dispersion Limit for Rational Initial Data: Generation of Dispersive Shock Waves

Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.
ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter D. Miller   +3 more
wiley   +1 more source

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
wiley   +1 more source

The Diophantine equation x2+2k=yn, II

International Journal of Mathematics and Mathematical Sciences, 1999
New results regarding the full solution of the diophantine equation x2+2k=yn in positive integers are obtained. These support a previous conjecture, without providing a complete proof.
J. H. E. Cohn
doaj   +1 more source

Diophantine equations involving factorials [PDF]

Mathematica Bohemica, 2017
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 and only
Horst Alzer, Florian Luca
doaj   +1 more source

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, Daniel Gutiérrez‐Ruiz, Diego Gonzalez, J. David Vergara   +3 more
wiley   +1 more source

The diophantine equation x2+3m=yn

International Journal of Mathematics and Mathematical Sciences, 1998
The object ofthis paper is to prove the following.
S. Akhtar Arif, Fadwa S. Abu Muriefah
doaj   +1 more source

Application of the group action approach to solving linear Diophantine equations [PDF]

Известия Саратовского университета. Новая серия: Математика. Механика. Информатика
The article substantiates a method for solving linear Diophantine equations using the theory of group actions. The purpose of this paper is to introduce actions of certain groups on the set of linear Diophantine equations and to study their ...
Chistov, Ivan Sergeevich, Tsybulya, Liliya Mikhailovna   +1 more
doaj   +1 more source

On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.
Alan Murat
doaj   +1 more source

On the moments of exponential sums over r$r$‐free polynomials

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
wiley   +1 more source