Let
$p$
be an odd prime number,
$K$
a
$p$
-adic field of degree
$r$
over
${{\mathbf{Q}}_{p}}$
,
$O$
the ring of integers in
$K,\,B\,=\,\{{{\beta }_{1}},\ldots .{{\beta }_{r}}\}$
an integral basis of
$K$
over
${{\mathbf{Q}}_{p}}$
,
$u$
a unit in
$O$
and consider sets of the form
$N\,=\,\{{{n}_{1}}{{\beta }_{1}}\,+\ldots +\,{{n}_{r}}{{\beta }_{r}}\,:\,1\,\le \,{{n}_{j}}\,\le \,{{N}_{j}},\,1\,\le \,j\,\le \,r\}$
. We show under certain growth conditions that the pair correlation of
$\{u{{z}^{2}}\,:\,z\,\in N\}$
becomes Poissonian.