Let n be a fixed non-zero integer and let \(m>1\) be a positive integer. We say a set \(\{a_1, a_2,..., a_m\}\) of positive integers is a \(D(n)-m-\textrm{tuple}\) if \(a_ia_j+n\) is a perfect square \(\forall i,j\in \{1, 2,..., m\}\) with \(i\not =j\) . By counting solutions to the congruence \(x^2\equiv {n}\hspace{0.1cm}\pmod {b}\) for \(b\in {\{1, 2,..., N\}}\) , we find the asymptotic behaviour of the number of D(n)-pairs and D(n)-triples with elements up to N. If n is a perfect square, these numbers grow as \(\frac{6}{\pi ^2}N\log N\) and \(\frac{3}{\pi ^2}N\log N\) , respectively. Otherwise, they grow as C(n)N and \(\frac{1}{2}C(n)N\) , where C(n) is a constant depending only on n which we determine as a function of some L-series of Dirichlet characters.
