In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$.

elementary-number-theory modular-arithmetic

All you need to know are the following facts: For $a \in \mathbb{Z}$, we have $$a^2 \equiv 0,1 \pmod2$$ $$a^2 \equiv 0,1 \pmod3$$ $$a^2 \equiv 0,\pm 1 \pmod5$$ Also, if $a^2 \equiv 0 \pmod{p}$, where $p$ is a prime, then $a \equiv 0 \pmod p$.

Now check each individual case and conclude what you want.

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