Investigation of one class of diophantine equations

• Date: 2000
• Main Authors: Bondarenko, A. V., Бондаренко, А. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4478
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the problem of existence of solutions of the equation \(\frac{X}{Y} + \frac{Y}{Z} + \frac{Z}{X} = m\) 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...