Diophantine triples with values in binary recurrences
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 4, pp. 579-608.

In this paper, we study triples $a,b$ and $c$ of distinct positive integers such that $ab+1,ac+1$ and $bc+1$ are all three members of the same binary recurrence sequence.

Classification : 11D72,  11D61,  11B37
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author = {Fuchs, Clemens and Luca, Florian and Szalay, Laszlo},
title = {Diophantine triples with values in binary recurrences},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {579--608},
publisher = {Scuola Normale Superiore, Pisa},
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Fuchs, Clemens; Luca, Florian; Szalay, Laszlo. Diophantine triples with values in binary recurrences. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 4, pp. 579-608. http://archive.numdam.org/item/ASNSP_2008_5_7_4_579_0/

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