This last example raises a question: how might one decide whether \(m \mid n\text{?}\) Of course, if you had a trusted calculator, you could ask it for the value of \(n \div m\text{.}\) If it spits out anything other than an integer, you know \(m \nmid n\text{.}\) This seems a little like cheating though: we don't have division, so should we really use division to check divisibility?
in-context