BG-MO 2005 Problem 6

Let $a,b$ and $c$ be positive integers such that $ab$ divides $c(c^{2}-c+1)$ and $a+b$ is divisible by $c^{2}+1$ . Prove that the sets $\{a,b\}$ and $\{c,c^{2}-c+1\}$ coincide.