You would think modding a negative number -x by m should really mean taking the mod of the inverse of x in Z_m. Additive modular inverse. Eg -2 mod 3 = 1. In Z_

You would think modding a negative number -x by m should really mean taking the mod of the inverse of x in Z_m. Additive modular inverse. Eg -2 mod 3 = 1. In Z_3 we have 1 + 2 = 3 = 0, so -2 -> 1.