Three-Pass Protocol number theory
I suspect that the professor is thinking of Quadratic Residuosity.  A value $x$ is a quadratic residue (modulo $p$) if there exists a $y$ such that $y^2 \equiv x \pmod p$.

This is important, because:


For any value $x$ (and prime $p$), it's easy to determine whether it's a quadratic residue or not.
If $e$ is relative prime to $p-1$, then $x^e$ is a quadratic residue iff $x$ is.


Now, if we have two plaintext messages, one of which is a quadratic residue, and one is not, can you see how the above observerations can be used to distinguish the two messages from any message in the 3-pass exchange?