The Diophantine equation a x 2 + 2 b x y − 4 a y 2 = ± 1

Lionel Bapoungué

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-13

Abstract:

We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation a x 2 + 2 b x y − 4 a y 2 = ± 1 , where a and b are nonnegative integers. The discussion is relative to the solution of Pell's equation v 2 − ( 4 a 2 + b 2 ) w 2 = − 4 .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:154343

DOI: 10.1155/S0161171203204348

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