Is there any way by which we can directly conclude whether a quadratic has integral roots or not?
Actually I was doing this question :
$$1 + 2 + 3 + 4 + ...... + n = kkk$$
Here I got $$n(1 + n)/2 = kkk$$
Since $kkk$ is always a multiple of $3$, so I put $kkk = 111$ and then checked if $$n(1 + n)/2 = 111$$ has an integral root or not.
Finally, I had to check till $kkk = 666$ which gave me $n = 36$
So, I want to know is there any quicker way by which I can just conclude by seeing if the quadratic has integral roots or not.
Sorry if my question is too vague or too trivial.