Question 164
a) Prove that if $p$, $q$, $\sqrt{2p-q}$ and $\sqrt{2p+q}$ are integers, then $q$ is even.
b) Find out how many positive integers $p$ have the property that both $\sqrt{2p-4030}$ and $\sqrt{2p+4030}$ are integers.
b) Find out how many positive integers $p$ have the property that both $\sqrt{2p-4030}$ and $\sqrt{2p+4030}$ are integers.