OIM 1991 Problem 5

Let $P(x, y)=2x^{2}-6xy+5y^{2}$ . Let us say an integer number $a$ is a value of $P$ if there exist integer numbers $b$ , $c$ such that $P(b, c)=a$ .

a) Find all values of $P$ lying between 1 and 100.

b) Show that if $r$ and $s$ are values of $P$ , then so is $rs$ .