Prove that the odd prime divisors of the integer $\displaystyle n^2 + n + 1 $ that are different from 3 are of the form 6k+1.

Proof.

Let p be an odd prime of $\displaystyle n^2 + n + 1 $ that is not 3, then $\displaystyle n^2 + n \equiv -1 \ (mod \ p)$

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