Problem

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

Tags: number theory, prime numbers



Is the following set of prime numbers $p$ finite or infinite, where each $p$ doesn't divide the numbers that can be expressed as $n^{2016}+2016^{2016}$ for $n\in \mathbb{N}$, if: a) $p=4k+3$; b) $p=4k+1$?