Journal of Integer Sequences, Vol. 13 (2010), Article 10.6.1

On the Shifted Product of Binary Recurrences

Omar Khadir
Department of Mathematics
University of Hassan II
Mohammedia, Morocco

Kálmán Liptai
Institute of Mathematics and Informatics
Eszterházy Károly College
Eger, Hungary

László Szalay
Institute of Mathematics and Statistics
University of West Hungary
Sopron, Hungary


The present paper studies the diophantine equation GnHn + c = x2n and related questions, where the integer binary recurrence sequences {G}, {H}, and {x} satisfy the same recurrence relation, and c is a given integer. We prove necessary and sufficient conditions for the solubility of GnHn + c = x2n. Finally, a few relevant examples are provided.

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(Concerned with sequences A000032 A000045 A001109 A001519 A001541 A001542.)

Received August 29 2009; revised version received April 29 2010; May 29 2010. Published in Journal of Integer Sequences, June 1 2010.

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