Question 39
Let $p(m, n)$ be the polynomial $2 m^{2} - 6 m n + 5 n^{2}$. The range of $p$ is the set of all integers $k$ such that $k = p(m, n)$ for some integers $m$, $n$. Find which members of $\{1,2, \ldots, 100\}$ are in the range of $p$. Show that if $h$ and $k$ are in the range of $p$, then so is $h k$.