I'm trying to prove using induction that 5^n-2^n is divisible by 3 for all values of n. I'm used to using induction to get k+1 within an expression that verifies a given formula, and have never used it to try and get to an answer divisible by 3.

So far I have 1 in the truth set because 5^1-2^1=5-2=3

And with a value k in the truth set

5^(k+1)-2^(k+1)=5(5^k)-2(2^k)

but don't know how i can further manipulate this or if i'm even on the right track.

If anyone could show me where to go from here i would be very grateful.