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Let $P(x, y)=2 x^2-6 x y+5 y^2$. We say that an integer $a$ is a value of $P$ if there exist integers $b, c$ for which $a=P(b, c)$.

(a) How many elements of $\{1,2, \ldots, 100\}$ are values of $P$ ?

(b) Prove that a product of values of $P$ is also a value of $P$.
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