notes-math-mod

i think when you are doing arithmetic in the integers mod something, it's not just the case that you can always do what you do in the normal numbers, rather i think that working with the negative numbers is different, in particular, division is different with them (is multiplication different too?).

Eg if you are mod 6, normally you can say "-2/2 = -1", but here, -2 = 6 - 2 = 4, so -2/2 = 4/2 = 2, and -1 = 6 - 1 = 5, and 2 != 5 mod 6.

i haven't checked this with others.

also i think the quadratic formula doesn't work if the modulus is even: http://math.stackexchange.com/a/261901/92670