Question

Prove that the square of any positive integer is of the form 3m or, 3m + 1 but not of the form 3m + 2.

Answer 1

To Prove: that the square of an positive integer is of the form 3m or 3m + 1 but not of the form 3m + 2.

Proof: Since positive integer n is of the form of 3q, 3q + 1 and 3q + 2

If n = 3q

If n = 3q + 1

Then, n² = (3q + 1)²

If n = 3q + 2

Then, n² = (3q + 2)²

Hence n² integer is of the form 3m, 3m + 1 but not of the form 3m + 2.