The Extendibility of Diophantine Pairs

Abstract

Let $n$ be a non-zero integer. A set $\{a_1, a_2,\cdots, a_m\}$ of $m$ distinct positive integers is called a Diophantine $m-tuples$ with the property $D(n),$ if $a_ia_j+n$ is a perfect square for all $1\leq i < j \leq m$. In this paper,we give some sets of polynomial with
integer coefficients, such that the product of any two of them added with a quadratic polynomial in $Z(n)$, is a square of
a polynomial with integer coefficients