Question. Use Euclid"s division lemma to show that the square of any positive integer is either of the form 3m or 3m+1.

[Hint: x be any positive integer then it is of the form 3q, 3q+1 or 3q+2. Now square of these and show that they can be rewritten in the form 3m or 3m+1.]

Ans. An integer can be of the form 3q, 3q+1 or 3q+2. Square all of these integers.