Results 51 to 60 of about 92,931 (194)

On the Exponential Diophantine Equation 2x+15y=z2

Annals of Pure and Applied Mathematics, 2022
In this article, we solve the exponential Diophantine equation 2 2 15 x y + = z where x y, and z are non-negative integers. The basic theorems in Number theory are given and applied to find all solutions.
S. Thongnak, W. Chuayjan, T. Kaewong
semanticscholar   +1 more source

Sums of three positive cubes

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
wiley   +1 more source

Random Diophantine equations in the primes II

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract Let d⩾2$d\geqslant 2$ and n⩾d$n\geqslant d$ with (d,n)∉{(2,2),(3,3)}$(d,n)\notin \lbrace (2,2),(3,3)\rbrace$. We consider homogeneous Diophantine equations of degree d$d$ in n+1$n+1$ variables and whether they have solutions in the primes.
Philippa Holdridge
wiley   +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

On the Exponential Diophantine Equation (132m) + (6r + 1)n = z2

Journal of scientific research, 2021
Nowadays, mathematicians are very interested in discovering new and advanced methods for determining the solution of Diophantine equations. Diophantine equations are those equations that have more unknowns than equations.
S. Aggarwal, S. Kumar
semanticscholar   +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

On the Exponential Diophantine Equation 15^x-17^y=z^2

International Journal of Latest Technology in Engineering Management & Applied Science
In this work, the exponential Diophantine equation 15x-17y=z2, where x,y and z are non-negative integers, was studied and presented with the theorems governing its expressions.
Wariam Chuayjan, Theeradach Kaewong, Sutthiwat Thongnak   +2 more
semanticscholar   +1 more source

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

Solution oSolution of Exponential Diophantine Equation nx +43y = z2, where n≡2(mod 129) and n+1 is not a Perfect Square

Journal of scientific research
Nowadays, researchers are very interested in studying various Diophantine equations due to their importance in Cryptography, Chemistry, Knot Theory, Astronomy, Geometry, Trigonometry, Biology, Algebra, Electrical Engineering, Economics, and Astrology ...
S. Aggarwal, A. T. Shahida
semanticscholar   +1 more source

Exact local distribution of the absolutely continuous spectral measure

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract It is well‐established that the spectral measure for one‐frequency Schrödinger operators with Diophantine frequencies exhibits optimal 1/2$1/2$‐Hölder continuity within the absolutely continuous spectrum (Avila and Jitomirskaya, Commun. Math. Phys. 301 (2011), 563–581).
Xianzhe Li, Jiangong You, Qi Zhou
wiley   +1 more source