Question 17
Let $m$ and $n$ be natural numbers and $p$ a prime number such that $m \lt n \lt p$. Furthermore:
$$
p \mid m^{2} + 1 \quad \text{ and } \quad p \mid n^{2} + 1
$$
Show that:
$$
p \mid m n - 1
$$
$$
p \mid m^{2} + 1 \quad \text{ and } \quad p \mid n^{2} + 1
$$
Show that:
$$
p \mid m n - 1
$$