Putnam 1982 B3

Let $p_n$ be the probability that $c+d$ is a perfect square when the integers $c$ and $d$ are selected independently at random from the set $\{1,2,\ldots,n\}$ . Show that $\lim_{n\to\infty}p_n\sqrt n$ exists and express this limit in the form $r(\sqrt s-t)$ , where $s$ and $t$ are integers and $r$ is a rational number.