Question

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

Answer 1

Answer:

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+1 or, a=3q+2

⇒a=3q or, a=3q+1 or, a=3q+2 for some integer q.