Investigation of one class of diophantine equations

• Дата: 2000
• Автори: Bondarenko, A. V., Бондаренко, А. В.
• Формат: Стаття
• Мова: Українська; Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2000
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/4478
• Назва журналу: 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...