Results 71 to 80 of about 446 (186)

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

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

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

Open Computer Science, 2018
We define a computable function f from positive integers to positive integers. We formulate a hypothesis which states that if a system S of equations of the forms xi· xj = xk and xi + 1 = xi has only finitely many solutions in non-negative integers x1, .
Tyszka Apoloniusz
doaj   +1 more source

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

The matrix diophantine equations $AX + BY = C$

Karpatsʹkì Matematičnì Publìkacìï, 2013
A method of constructing of solutions of matrix Diophantine equations $AX + BY = C$ over commutative domains of finitely generated principal ideals is suggested. The formulas of general solutions of such equations in some cases is proposed. The criterion
N. S. Dzhaliuk, V. M. Petrychkovych
doaj   +1 more source

Multiplicative Diophantine equations

Journal of Number Theory, 1992
The solution of the diophantine equation \(\prod_{i=1}^ n x_ i= \prod_{i=1}^ n y_ i\) is given in terms of \(n^ 2\) parameters (Bell's theorem) [cf. the first author, Proc. Ramanujan Cent. Int. Conf., Annamalainagar/India 1987, RMS Publ. 1, 141-146 (1988; Zbl 0696.10014)].
Srinivasa Rao, K., Santhanam, T.S., Rajeswari, V.   +2 more
openaire   +1 more source

Diophantine equations in separated variables and polynomial power sums. [PDF]

Mon Hefte Math, 2021
Fuchs C, Heintze S.
europepmc   +1 more source

The diophantine equation r2+r(x+y)=kxy

International Journal of Mathematics and Mathematical Sciences, 1985
The Diophantine equation of the title is solved in integers.
W. R. Utz
doaj   +1 more source

On a Diophantine equation of Erdös

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994
The second lemma is not proved in the quoted paper. It would lead to a polynomial bound in the height of the binary form. Despite this the main results can be true.
openaire   +3 more sources

Diophantine Solutions Based Permutation for Image Encryption

Journal of Algorithms & Computational Technology, 2013
A permutation technique based on the resolution of the system of three independent Diophantine equations is presented. Each Diophantine equation parameters are two positive integers generated from a chaotic system.
J. S. Armand Eyebe Fouda, J. Yves Effa, Bertrand Bodo, Maaruf Ali   +3 more
doaj   +1 more source