Question 21
Let $p$ be a prime number of the form $p = 12k + 5$ and let $\{A_n\}_{n=1}^{\infty}$ be a sequence given by $A_n = (n^1 - 1)(n^2 - 1) \cdots (n^{6k+1} - 1)(n^{6k+2} - 1)$. Show that
$$
A_2^2 + A_8^2 \equiv 0 \pmod{p}.
$$
$$
A_2^2 + A_8^2 \equiv 0 \pmod{p}.
$$