Question 42
Let $a\in\mathbb N$, with $a\gt2$. Prove the following statements.
- **(a)** There exists a composite integer $n\gt1$ such that $a^n\equiv1\pmod n$.
- **(b)** If $p$ is the smallest integer greater than $1$ for which $a^p\equiv1\pmod p$, then $p$ is prime.
- **(c)** There is no integer $n\gt1$ such that $2^n\equiv1\pmod n$.
- **(a)** There exists a composite integer $n\gt1$ such that $a^n\equiv1\pmod n$.
- **(b)** If $p$ is the smallest integer greater than $1$ for which $a^p\equiv1\pmod p$, then $p$ is prime.
- **(c)** There is no integer $n\gt1$ such that $2^n\equiv1\pmod n$.