On the number of solutions of the diophantine equation x2 + 2a - pb = y4

Abstract

Let p be a fixed odd prime. In this paper, we study the integer solutions (x, y, a, b) of the equation x2 +2a · pb = y4; gcd(x, y) = 1, x > 0; y > 0; a ≥ 0; b ≥ 0, and we derive upper bounds for the number of such solutions.AMS 2010 Subject Classifcation: 11D61.