Geodesic
ON THE FAMILY OF DIOPHANTINE TRIPLES {k − 1, k + 1, 16k 3 − 4k}
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 333-344

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DOI

It is proven that if k ≥ 2 is an integer and d is a positive integer such that the product of any two distinct elements of the set increased by 1 is a perfect square, then d = 4k or d = 64k 5−48k 3+8k. Together with a recent result of Fujita, this shows that all Diophantine quadruples of the form {k − 1, k + 1, c, d} are regular.
DOI : 10.1017/S0017089507003564
Mots-clés : 11D09, 11D25, 11J86, 11Y50 
BUGEAUD, YANN; DUJELLA, ANDREJ; MIGNOTTE, MAURICE. ON THE FAMILY OF DIOPHANTINE TRIPLES {k − 1, k + 1, 16k 3 − 4k}. Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 333-344. doi: 10.1017/S0017089507003564
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     journal = {Glasgow mathematical journal},
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