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On the Shifted Product of Binary Recurrences
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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

**Abstract:**

The present paper studies the diophantine equation
*G*_{n}*H*_{n} +
*c* = *x*_{2n} 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
*G*_{n}*H*_{n} + *c* = *x*_{2n}. 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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