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Great forum, I have been reading some cool stuff here for about a month.

Heres my question:

Using induction prove that 5 divides 8^n - 3^n, n Natural Number.

I know its true for n = 1, but I get stuck on the n = k+1. I dont know how to proceed from here: 8(8^k) - 3(3^k)

Also, I KNOW this is very easy using mod 5 but I can't do it here, I HAVE to prove it using only induction.

Any hints?

Thanks,

-William