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