On the exponential Diophantine equation $x^2+p^m{q}^n=2y^p$

Abstract

We study the exponential Diophantine equation $x^2+p^m{q}^n=2y^p$ in positive integers $x,y,m,n$, and odd primes $p$ and $q$ using primitive divisors of Lehmer sequences in combination with elementary number theory. We discuss the solvability of this equation.

10 pages. To appear in `New Zealand J. Math.'