Comment by tialaramex

I say you want a pair of operations such that (a, b) = quotient_and_remainder(x, y) gives you a and b such that a * y + b = x

The Euclidean division and remainder work, the other division and remainder also work, and they're both identical for the positive integers so people who only think about the positive integers won't even notice there's a choice here. So I like that Rust provides both pairs, in the same way Rust provides both Wrapping<T> and Saturating<T> because maybe you mean wrapping overflow or maybe you mean saturating overflow and we should make you choose not just assume we know best.