Question

If n is a positive integer prove that when we divide n^2 by 5 we get that r=0,1 or 4

Answer 1

In case you are wondering r would be the remainder in elementary divison

Answer 2

consider n = 5k, 5k+1, 5k+2, 5k+3, 5k+4

Answer 3

work the 5 cases separately

Answer 4

Right, oops.....I totally should have seen splitting it up that way and not the way I did....lol thanks

Answer 5

Will close when I fully solve

Answer 6

np :) thats one way, there is another nice way if you're allowed to use congruences