EN
Let m be a positive integer. Using an upper bound for the solutions of generalized Ramanujan-Nagell equations given by Y. Bugeaud and T. N. Shorey, we prove that if 3 ∤ m, then the equation $(4m²+1)^x + (5m²-1)^y = (3m)^z$ has only the positive integer solution (x,y,z) = (1,1,2).