In RSA, a message is encrypted by $m^e \pmod N$. $N$ is the modulus, $m$ is the message and $e$ is the public exponent. (I know that $m$ should not be greater than $N$.)
My question is, can $m^e$ be greater than $N$ (obviously, before taking the modulus)?
In that case is there a possibility like $ m_1^e=m_2^e \pmod N$, i.e. can we get a collision?