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

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- Mar 23rd 2009, 11:53 AMhmmmmproof by induction
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 - Mar 23rd 2009, 01:18 PMTwistedOne151
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.