Results 51 to 60 of about 20,685 (194)

On the exceptional set in Littlewood's discrete conjecture

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
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

Tessellation Groups, Harmonic Analysis on Non‐Compact Symmetric Spaces and the Heat Kernel in View of Cartan Convolutional Neural networks

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, Federico Milanesio, Marcelo Oyarzo, Matteo Santoro, Mario Trigiante   +4 more
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

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

Diophantine Equation [PDF]

, 2010
In the first chapter we have given some definations, theorems, lemmas on Elementary Number Theory. This brief discussion is useful for next discussion on the main topic.
Panda, Sagar
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

The Polynomial Solutions of Quadratic Diophantine Equation X2−ptY2+2KtX+2ptLtY = 0

Journal of Mathematics, 2021
In this study, we consider the number of polynomial solutions of the Pell equation x2−pty2=2 is formulated for a nonsquare polynomial pt using the polynomial solutions of the Pell equation x2−pty2=1.
Hasan Sankari, Ahmad Abdo
doaj   +1 more source

A hypothetical upper bound for the solutions of a Diophantine equation with a finite number of solutions

, 2013
We conjecture that if a system S \subseteq {x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in integers x_1,...,x_n, then each such solution (x_1,...,x_n) satisfies |x_1|,...,|x_n| \leq 2^{2^{n-1}}.
Tyszka, Apoloniusz
core   +1 more source

GCD inequalities arising from codimension‐2 blowups

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract Assuming a deep Diophantine geometry conjecture by Vojta, Silverman proved an inequality giving an upper bound for the greatest common divisor (GCD). In this paper, we unconditionally prove a weaker version of this inequality. The main ingredient is the Ru–Vojta theory, which provides an efficient method of using Schmidt subspace theorem.
Yu Yasufuku
wiley   +1 more source