Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.4

Integer Solutions of the Equation y2 = Ax4 + B


Paraskevas K. Alvanos
1st Model and Experimental High School of Thessaloniki
Kleanthous 30
54453 Thessaloniki
Greece

Konstantinos A. Draziotis
Department of Informatics
Aristotle University of Thessaloniki
54124 Thessaloniki
Greece

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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(Concerned with sequences A000129 A001076.)

Received November 4 2014; revised versions received January 31 2015; February 23 2015. Published in Journal of Integer Sequences, May 12 2015.

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