If you used Clearing in 2024, how did you find it?

How do I use proof by induction on this, specifically using f(k+1)-f(k)?

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.

Reply 1

mqb2766

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.

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.