MathNet 2001 — Part 02 Question 8

Let be given a positive integer $n$ and two coprime integers $a, b$ greater than $1$. Let $p, q$ be two odd divisors greater than $1$ of $a^{6n} + b^{6n}$. Find the remainder of the division of $p^{6n} + q^{6n}$ by $6 \cdot (12)^n$.