On the family of Diophantine triples \(\{k+1,4k,9k+3\}\)
The paper provides an extendibility result concerning a parametric family of Diophantine triples. The authors prove that if \(k\) and \(d\) are positive integers such that the product of any two distinct elements of the set \(\{k+1,4k,9k+3,d\}\) increased by \(1\) is a perfect square, then \(d=144k^3+192k^2+76k+8\).
scientific article; zbMATH DE number 5651911
scientific article