A problem by GH Hardy

Algebra Level 2

11, 21, 12, 31, 22, 13, 41, 32, 23, 14, \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 18871920\frac {1887}{1920} is the mthm^\text{th} term and 17892018\frac {1789}{2018} is the nthn^\text{th} term of the sequence above, find mn.|m-n|.

Note: In this sequence, the fractions do not reduce. For example, 22\frac{2}{2} is distinct from 11.\frac{1}{1}.

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