Question 128
Find all triples $(p, q, n)$ such that
$$
q^{n+2} \equiv 3^{n+2} \pmod{p^n}, \quad p^{n+2} \equiv 3^{n+2} \pmod{q^n}
$$
where $p$, $q$ are positive odd primes and $n \gt 1$ is an integer.
$$
q^{n+2} \equiv 3^{n+2} \pmod{p^n}, \quad p^{n+2} \equiv 3^{n+2} \pmod{q^n}
$$
where $p$, $q$ are positive odd primes and $n \gt 1$ is an integer.