Annals of Mathematics

Number Theory Level 3

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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