On the Diophantine equation nx2+22m=yn

Let n be a fixed odd integer with n>1. In this paper, using a recent result on the existence of primitive divisors of Lehmer numbers give by Y. Bilu, G. Hanrot and P.M. Voutier, we prove that the equation nx2+22m=yn has no positive integer solution (x,y,m) with gcd(x,y)=1.