Prove using mathematical induction that 23n 1 is divisible b

Prove using mathematical induction that 23n- 1 is divisible by 7 for all n N.

A. Show that the base step is true

B. What is the inductive hypothesis?

C. What do we have to show?

D. Proof proper (Justify each step)

As in this question,

Let the given statement be P(n) , i.e.

P(n)= 23n-1 is divisible by 7

It can be observed that P(n) is true for n=1

So by putting n=1 in above equation

P(n) = 23(1)-1 = 22

hence, 22 is not divisible by 7

Lets put n=2,

P(n) = 23(2)-1 = 46-1 = 45

hence, 45 is also not divisible by 7.

So, we can not prove using mathematical induction as P(n) is not true for n=1.