Integer Solutions of the Equation y 2 = Ax 4 + B

Abstract

Let A ∈ {k2(k2l2 + 1), 4k2(k2(2l − 1)2 + 1)}, where k and l are positive integers, and let B be a non-zero square-free integer such that |B| < √ A. In this paper we determine all the possible integer solutions of the equation y2 = Ax4 + B by using terms of Lucas sequences of the form mx2. 

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