Geodesic
On the shifted product of binary recurrences
Journal of integer sequences, Tome 13 (2010) no. 6
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 
@article{JIS_2010__13_6_a3,
     author = {Khadir,  Omar and Liptai,  K\'alm\'an and Szalay,  L\'aszl\'o},
     title = {On the shifted product of binary recurrences},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {6},
     zbl = {1250.11021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_6_a3/}
}
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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/