Question

Show that any positive integer is of the form 3q or 3q+1 or 3q+2 for some integer q.

Answer 1

Euclid's Division Lemma : For any two positive integers a and b, there exists two unique integers q and r such that a = bq + r, 0 r < b.
If we take b = 3, the possible values of r will be 0, 1 and 2
Hence, either a = 3q or a = 3q + 1 or a = 3q + 2.