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in Principle of Mathematical Induction by (46.2k points)

Prove that 23n – 1 is divisible by 7.

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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.

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