Take an odd integer; square it; then divide by 8. Can the remainder by 3? Can it be 7? (of course, just "yes" or "no" is not an acceptable answer. You must explain why the proposed remainder can or cannot occur.)

Please Help...

I have this so far:

Ex. (3)(3) = 9/8 = 1.125

Wanted to try and get to 3 so I went up with my integer

Ex. (7)(7) = 49/8 = 6.125

Ex. (9)(9) = 81 / 8 = 10.125

I am assuming that this will not work....but am not certain. Does anyone have any other thoughts?