Question: prove 4^n-1 is divisible by 3?
Answer: Yes 3 is divisible by 3. If 4^n-1 is divisible by 3, it can be written as 4^n -1 = 3*k, where k is an integer. ... 4*k + 1 is an integer since k is an integer, so 4^(n+1) -1 is divisible by 3.