Investigation of one class of diophantine equations

Authors

  • A. V. Bondarenko

Abstract

We consider the problem of existence of solutions of the equation XY+YZ+ZX=m in natural numbers for differentmN. We prove that this equation possesses solutions in natural numbers form=a 2+5,aZ, and does not have solutions ifm=4p 2,pN, andp is not divisible by 3. We also prove that, forn≥12, the equation b1b2+b2b3++bn1bn+bnb1=m possesses solutions in natural numbers if and only ifmn,mN.

Published

25.06.2000

Issue

Section

Research articles

How to Cite

Bondarenko, A. V. “Investigation of One Class of Diophantine Equations”. Ukrains’kyi Matematychnyi Zhurnal, vol. 52, no. 6, June 2000, pp. 831–836, https://umj.imath.kiev.ua/index.php/umj/article/view/4478.