# proof by induction

• Mar 23rd 2009, 12:53 PM
hmmmm
proof 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, 02:18 PM
TwistedOne151
1. Find $7^n+4^n+1^n$ for n=1, and show it is divisible by 6.

2. Find $\left(7^{n+1}+4^{n+1}+1^{n+1}\right)-\left(7^n+4^n+1^n\right)$. Use it to show that $7^{n+1}+4^{n+1}+1^{n+1}$ is divisible by 6 if $7^n+4^n+1^n$ is.

--Kevin C.