If $a,b$ and $n$ are natural numbers then $a^{n-1}+b^{n-1}$ is divisible by:

Question

$$\begin {array} {1 1} (a)\;a+b & \quad (b)\;a-b \\ (c)\;a^3+b^3 & \quad (d)\;a^2+b^2\end {array}$$