Question 104
Let $n$ be a natural number and $p, q$ primes such that the following statements hold:
$$
\begin{gathered}
p q \mid n^{p}+2 \\
n+2 \mid n^{p}+q^{p}
\end{gathered}
$$
Show that there exists a natural number $m$ such that $q \mid 4^{m} n+2$.
$$
\begin{gathered}
p q \mid n^{p}+2 \\
n+2 \mid n^{p}+q^{p}
\end{gathered}
$$
Show that there exists a natural number $m$ such that $q \mid 4^{m} n+2$.