Determine all positive integers $a$ and $b$ for which $a^4 + 4b^4$ be a prime number.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N2 day1
Tags: prime, number theory
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N2 day1
Tags: prime, number theory
Determine all positive integers $a$ and $b$ for which $a^4 + 4b^4$ be a prime number.