On the diophantine equation -: (x3-1)/(x-1)=(yn-1)/(y-1)

In this paper we prove that the equation (x(3) - 1)/(x - 1) = (y(n) - 1)/(y - 1), x,y,n is an element of 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.