What a Proof Is · Challenge problem

The lesson proved: if $3 \mid a^2 + b^2$, then $3 \mid a$ and $3 \mid b$. A student copies the proof with another prime in place of $3$. What is the smallest prime $p$ for which "if $p \mid a^2 + b^2$, then $p \mid a$ and $p \mid b$" is FALSE?