Question 2
Let $p$ be a prime number.
Prove that there exists a prime number $q$ such that $n^{p} \not\equiv p \pmod{q}$ for every $n \in \mathbb{Z}$.
Prove that there exists a prime number $q$ such that $n^{p} \not\equiv p \pmod{q}$ for every $n \in \mathbb{Z}$.