Original post by maybemiro

Prove f(n)=2^n+6^n is divisible by 8.

I normally use f(k+1)-f(k) to prove such statements, however I am stuck on this question.

I normally use f(k+1)-f(k) to prove such statements, however I am stuck on this question.

Is it an induction question? Probably easier to do with other methods but you could note that the n+1 step is

2.2^n + 6.6^n

So can you "add 0" to this, so add/subtact a 2^n term which makes the inductive argument go?

Or split the 6.6^n term up along the same lines. You can subtract the nth term but its just an extra step without any advantage.

(edited 10 months ago)

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