Annals of Mathematics

All the solutions of the following equation \({ m }^{ 2 }-3m+1={ n }^{ 2 }+n-1\) where \(m,n\) are positive integers can be written as \((n,m)\).

Find the value of \( | m-n| \).

\[\] Notation: \( | \cdot | \) denotes the absolute value function.

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