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.