TITLE: Is $83^{27} +1 $ a prime number?
QUESTION [16 upvotes]: I'm having problems with exercises on proving whether or not a given number is prime. Is $83^{27} + 1$ prime?

REPLY [4 votes]: well it is divisible by $84$ and in general $\forall a,m\in\mathbb {N}$ we have
$(a+1)\mid (a^{2m+1}+1)$ So....