Investigation of one class of diophantine equations
Abstract
We consider the problem of existence of solutions of the equation XY+YZ+ZX=m in natural numbers for differentm∈N. We prove that this equation possesses solutions in natural numbers form=a 2+5,a∈Z, and does not have solutions ifm=4p 2,p∈N, andp is not divisible by 3. We also prove that, forn≥12, the equation b1b2+b2b3+⋯+bn−1bn+bnb1=m possesses solutions in natural numbers if and only ifm≥n,m∈N.Downloads
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.