Geodesic
On the shifted product of binary recurrences
Journal of integer sequences, Tome 13 (2010) no. 6.

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Summary: 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.
Classification : 11B39, 11D61
Keywords: binary recurrence 
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     author = {Khadir, Omar and Liptai, K\'alm\'an and Szalay, L\'aszl\'o},
     title = {On the shifted product of binary recurrences},
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     year = {2010},
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Khadir, Omar; Liptai, Kálmán; Szalay, László. On the shifted product of binary recurrences. Journal of integer sequences, Tome 13 (2010) no. 6. http://geodesic.mathdoc.fr/item/JIS_2010__13_6_a3/