As is well known, division of integers with remainder can be defined in different ways. The definition in Wolfram and the definition in theoretical mathematics are different. How to express traditional division with remainder in Wolfram? Here is a variant solution:
quotient[m_, n_] := (m - Mod[m, Abs[n]])/n
remainder[m_, n_] := Mod[m, Abs[n]]
Is there anything more elegant?
