Question

Prove that energy positive integer is of the form 3p,3p+1 or 3p+2, whaere p is any integer.

Answer 1

Let n be any positive integer.

On dividing n by 3, p be the quotient and r be the remainder.

n=3p+r, where 0≤r<3

⇒n=3p or (3p+1) or (3p+2) for some integer p.

Thus, any positive integer is of the form 3p or (3p+1) or (3p+2) for some integer p.