A NOTE ON DUJELLA’S UNICITY CONJECTURE

Abstract

Using properties of binary quadratic Diophantine equa-tions, we prove that if r = pmqn, where p, q are distinct odd primes and m, n are positive integers, then the equation x2 −(r2 + 1) y2 = r2 has at most one positive integer solution (x, y) with y < r − 1.