Question

Prove the statement by principle of mathematical induction:

22n - 1 is divisible by 3​

Answer 1

Step-by-step explanation:

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. Sub in 3k = 4^n -1 to get 4*(3*k + 1) -1 = 12 *k + 4 - 1 = 12 *k +3 = 3*(4*k + 1). 4*k + 1 is an integer since k is an integer, so 4^(n+1) -1 is divisible by 3.