  For an element $r$ of a ring $R$, a Diophantine $D(r)$ $m$-tuple is an
$m$-tuple $(a_1,a_2,\ldots,a_m)$ of elements of $R$ such that for all $i,j$
with $i\neq j$, $a_ia_j+r$ is a perfect square in $R$. In this article, we
compute and estimate the measures of the sets of $D(r)$ $m$-tuples in the ring
$\mathbb{Z}_p$ of $p$-adic integers, as well as its residue field
$\mathbb{F}_p$.
