On the family of Diophantine triples {k+2,4k,9k+6}

Filipin, Alan and Togbé, Alain (2009) On the family of Diophantine triples {k+2,4k,9k+6}. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 25 (2). pp. 145-153. ISSN 0866-0174

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Abstract

In this paper, we prove that if k and d are two positive integers such that the product of any two distinct elements of the set {k+2, 4k, 9k+6,d\} increased by 4 is a perfect square, then d=36k^3 + 96k^2 + 76k + 16.

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