Showing that the square of any integer is of the form $3k$ or $3k+1$ for some integer $k$

Question

Show that the square of every integer is of the form $3k$ or $3k + 1$, for some $k\in\mathbb{Z}$. Conclude that $3n^2-1$ is never a perfect square.

Sorry if I do not attach my effort. The truth is I am new to this. I would appreciate any help !!!

Welcome to Mathematics Stack Exchange. Here is a MathJax tutorial — J. W. Tanner, Oct 23 '20 at 00:27

score 1 · Answer 1 · answered Oct 23 '20 at 00:25

1

Hint: Every integer is of the form $3k$, $3k+1$, or $3k+2$. What do you get when you square those?

answered Oct 23 '20 at 00:25

J. W. Tanner

1 Answers1