Abstract:

In this paper, we consider the generalized Ramanujan-Nagell equation x^2 + (6R_k - 1)^m = (3R_k)^n involving Near-Repdigits and we show that, under some conditions, it has only the positive integer solution (x,m,n)=(3R_{k}-1, 1, 2). The proof is based on the Jacobi Symbol and Zsigmondy's theorem.