Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 25, No. 2, pp. 145-153 (2009)

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

Alan Filipin and Alain Togbé

University of Zagreb, Croatia; Purdue University North Central, USA

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 $d=36k^3 + 96k^2 + 76k + 16$.

Keywords: Diophantine m-tuples, Pell equations, Baker's method

Classification (MSC2000): 11D09; 11D25, 11J86

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