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Prove by method of induction 152n-1 + 1 is divisible by 16, for all n ∈ N.

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152n-1 + 1 is divisible by 16, if and only if

(152n+1 + 1) is is a multiple of 16.

Let P(n) ≡ 152n-1 + 1 = 16m, where m ∈ N.

Step IV:

From all the steps above, by the principle of mathematical induction, P(n) is true for all n ∈ N.

∴ 152n-1 + 1 is divisible by 16, for all n ∈ N.

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