TITLE: Prove that all prime divisors of $7a^2(a+1)-1$ are of the form $7k\pm1$
QUESTION [11 upvotes]: Question:

Let a be a positive integer. Prove that all prime divisors of $7a^2(a+1)-1$ are of the form $7k\pm1$

$a$ and $k \in \mathbb{N}$ .

REPLY [4 votes]: It gets complicated, but this is Corollary 10 in this paper on cubic reciprocity.