Statement P(n) : 23n – 1 is divisible by 7
i.e., 23n – 1 = 7n
For n = 1, P(1)= 23(1) – 1 = 7 is divisible by 7
Hence, given statement is true for n = 1,
i.e., P(1) is true.
Let P(m) is true, i.e. 23m – 1 = 7m ……(i)
Now, we have to prove that given statement is also true for n = m + 1
i.e.. P(m + 1) is true
i.e., 23(m+1) – 1, is divisible by 7.
⇒ P(m + 1) is true.
Hence, the given statement P(n) is true for each value of n.
Hence Proved.