Let $a,b,c\in\mathbb{N}$ prove that if there is a polynomial $P,Q,R\in\mathbb{C}[x]$, which have no common factors and satisfy $$P^a+Q^b=R^c$$and $$\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}>1.$$ (tatari/nightmare)
Problem
Source: Mathcenter Contest / Oly - Thai Forum 2010 R1 p1 https://artofproblemsolving.com/community/c3196914_mathcenter_contest
Tags: polynomial, algebra