prove by induction that (7^n)+(4^n)+(1^n) is divisible by six for all n greater than or equal to one
thanks for any help
1. Find $\displaystyle 7^n+4^n+1^n$ for n=1, and show it is divisible by 6.
2. Find $\displaystyle \left(7^{n+1}+4^{n+1}+1^{n+1}\right)-\left(7^n+4^n+1^n\right)$. Use it to show that $\displaystyle 7^{n+1}+4^{n+1}+1^{n+1}$ is divisible by 6 if $\displaystyle 7^n+4^n+1^n$ is.
--Kevin C.