ON THE FAMILY OF DIOPHANTINE TRIPLES {k− 1,k+ 1, 16k3− 4k}

Author:

BUGEAUD YANN,DUJELLA ANDREJ,MIGNOTTE MAURICE

Abstract

AbstractIt is proven that ifk≥ 2 is an integer anddis a positive integer such that the product of any two distinct elements of the setincreased by 1 is a perfect square, thend= 4kord= 64k5−48k3+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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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