Find all integers $n \ge 2$ for which $\sqrt[n]{3^n+ 4^n+5^n+8^n+10^n}$ is an integer.
Source: 2011 Saudi Arabia Pre-TST January p3
Tags: number theory, radical, Integer
Find all integers $n \ge 2$ for which $\sqrt[n]{3^n+ 4^n+5^n+8^n+10^n}$ is an integer.