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On the diophantine equation
Authors:Maohua Le
Institution:Department of Mathematics, Zhanjiang Teachers College, Postal Code 524048, Zhanjiang, Guangdong, P. R. China
Abstract:In this paper we prove that the equation $(x^3-1)/(x-1)=$ $(y^n-1)/(y-1)$, $x,y,n\in\mathbb{N}$, $x>1$, $y>1$, $n>3$, has only the solutions $(x,y,n)=(5,2,5)$ and $(90,2,13)$ with $y$ is a prime power. The proof depends on some new results concerning the upper bounds for the number of solutions of the generalized Ramanujan-Nagell equations.

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