Results 61 to 70 of about 92,931 (194)

On the Exponential Diophantine Equation 2^x+1245^y=z^2

International Journal of Latest Technology in Engineering Management & Applied Science
Let x,yand z be non-negative integers. We solve the exponential Diophantine equation 2^x+1,245^y=z^2.  The result indicates that the equation has a unique solution,(x,y,z)=(3,0,3).
Theeradach Kaewong, Wariam Chuayjan, Sutthiwat Thongnak   +2 more
semanticscholar   +1 more source

Linear Diophantine equations and conjugator length in 2‐step nilpotent groups

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract We establish upper bounds on the lengths of minimal conjugators in 2‐step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diophantine equations. We prove that in some cases these bounds are sharp.
M. R. Bridson, T. R. Riley
wiley   +1 more source

Tian’s Conjecture on the Prime Factorization of the Binomial Coefficient $\mathbf{\left(}{\displaystyle \genfrac{}{}{0pt}{}{\mathit{n}\mathbf{+}\mathbf{1}}{\mathbf{2}}}\mathbf{\right)}$

Mathematics
Tian’s conjecture states that for any fixed distinct prime numbers p1,…,pm, the Diophantine equation n+12=p1α1·p2α2···pmαm in positive integers n,α1,…,αm has at most m solutions.
Zhenbing Zeng, Ákos Pintér, Xinchu Fu, Jianjun Paul Tian   +3 more
doaj   +1 more source

On Some Mixed Polynomial Exponential Diophantine Equation: \(\alpha^n+\beta^n+a(\alpha^s\pm\beta^s)^m+D=r(u^k+v^k+w^k)\) with \(\alpha\) and \(\beta\) Consecutive

Journal of Advances in Mathematics and Computer Science
Let \(a,\alpha,\beta,r,u,v,w\) and \(D\) be any integers and suppose that \(n,m,s\) and \(k\) are non-negative exponent. In thispaper, the diophantine equation \(\alpha^n+\beta^n+a(\alpha^s\pm\beta^s)^m+D=r(u^k+v^k+w^k)\) is developed and investigated ...
Lao Hussein Mude
semanticscholar   +1 more source

Arithmetic progressions at the Journal of the LMS

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We discuss the papers P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. (1) 11 (1936), 261–264 and K. F. Roth, On certain sets of integers, J. London Math. Soc. (1) 28 (1953), 104–109, both foundational papers in the study of arithmetic progressions in sets of integers, and their subsequent influence.
Ben Green
wiley   +1 more source

On the Exponential Diophantine Equation 305^x+503^y=z^2

International Journal of Latest Technology in Engineering, Management & Applied Science
In this paper, we compute and prove the solution to the exponential Diophantine equation 305^x+503^y=z^(2 )where x,y and zare non-negative integers. The result indicate that the equation has no solution.
T. Kaewong, S. Thongnak, W. Chuayjan
semanticscholar   +1 more source

Jeśmanowicz' conjecture on exponential diophantine equations

Functiones et Approximatio Commentarii Mathematici, 2011
Jeśmanowicz' conjecture is the following statement: If \(a\), \(b\), \(c\) are coprime positive integers such that \(a^2+b^2=c^2\) with even \(b\), then the exponential equation \(a^x+b^y=c^z\) has the only solution \((x,y,z)=(2,2,2)\) in positive integers. This paper contains various new results on this conjecture.
openaire   +2 more sources

Diophantine tuples and product sets in shifted powers

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley   +1 more source

On the Exponential Diophantine Equation 17^x – 11^y = z^2

International Journal of Latest Technology in Engineering, Management & Applied Science
In this work, we study all solutions to the exponential Diophantine equation 17x – 11y = z2 where x, y and z are non-negative integers. The result indicates that there are two solutions, which are (x, y, z) Σ {(0, 0, 0), (1, 0, 4)}.
T. Kaewong, W. Chuayjan, S. Thongnak
semanticscholar   +1 more source

A universal example for quantitative semi‐uniform stability

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract We characterise quantitative semi‐uniform stability for C0$C_0$‐semigroups arising from port‐Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port‐Hamiltonian C0$C_0$‐semigroups exhibiting arbitrary decay rates slower than t−1/2$t^{-1/2}$.
Sahiba Arora, Felix L. Schwenninger, Ingrid Vukusic, Marcus Waurick   +3 more
wiley   +1 more source