Question 7
Let $S_r(n) = 1^r + 2^r + \dots + n^r$ where $r$ is a rational number and $n$ is a positive integer. Find all triples $(a, b, c)$ where $a$ and $b$ are positive rational numbers and $c$ is a positive integer for which there exist infinitely many positive integers $n$ satisfying $S_a(n) = (S_b(n))^c$.