As a challenge, we were shown an RSA setup where we have a big $n$ (617 decimal digits), $e=4$, and asked to recover three messages. (However, the messages are padded to the same length as the key with random bytes.)
I don't have a very strong background in cryptography, and this is apparently so poor that nobody bothered to explain how you'd wreck it. For instance, I've been reading the Wikipedia article on Coppersmith's attack, and it reads:
[e=3, 17 or 65537] are chosen because they make the modular exponentiation operation faster. Also, having chosen such e, it is simpler to test whether $gcd(e, p-1)=1$ and $gcd(e, q-1)=1$ while generating and testing the primes in step 1 of the key generation.
I'm not super good at this, but given that $e$ is even, I'm pretty sure that it can't be coprime with $p-1$ or $q-1$.
How would I go around to crack it?
EDIT: as some of you have guessed, this was not RSA. Instead, the single number $p$ was a ~2048 bits prime. The crypted message was essentially $pad(m)^4 \mod p$, which could be deciphered using the modular square root twice.