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

[摘要] 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 $d=36k^3 + 96k^2 + 76k + 16$.

[学科分类] 数学（综合）

[关键词] Baker's method