Question

Show any positive integer is in form of 3q or 3q+1 for integer q

Answer 1

Let a be any positive integer and b=3. Applying division lemma with a and b=3, we have         a = 3q +r, where 0 ≤ r ≤ 3 and q is some integer => a = 3q + 0 or, a = 3q + 2
 =>   a = 3q or, a = 3q + 2 for some integer q.