Determine all triples of natural numbers $(a,b, c)$ with $b> 1$ such that $2^c + 2^{2016} = a^b$.
Source: Indonesia MO (INAMO) 2016 P2
Tags: Diophantine equation, number theory
Determine all triples of natural numbers $(a,b, c)$ with $b> 1$ such that $2^c + 2^{2016} = a^b$.