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Prove by method of induction 52n – 22n is divisible by 3, for all n ∈ N.

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52n - 22n is divisible by 3, if and only if

(52n - 22n) is a multiple of 3.

Let P(n) = (52n - 22n) = 3m, where m ∈ N.

Step IV:

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

\(\therefore\) 52n - 22n is divisible by 3, for all n ∈ N.

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