A problem by GH Hardy

Algebra Level 2

\[\frac 1{1},\ \frac {2}{1},\ \frac {1}{2},\ \frac {3}{1},\ \frac {2}{2},\ \frac {1}{3},\ \frac {4}{1},\ \frac {3}{2},\ \frac {2}{3},\ \frac {1}{4},\ \ldots \]

If \(\frac {1887}{1920}\) is the \(m^\text{th}\) term and \(\frac {1789}{2018}\) is the \(n^\text{th}\) term of the sequence above, find \(|m-n|.\)

Note: In this sequence, the fractions do not reduce. For example, \(\frac{2}{2}\) is distinct from \(\frac{1}{1}.\)

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