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Find all pairs of positive integers

Source: Singapore MO 2011 open round 2 Q5

July 2, 2011
modular arithmeticalgebrafunctiondomainnumber theory proposednumber theory

Problem Statement

Find all pairs of positive integers (m,n)(m,n) such that m+n−3mnm+n=20113.m+n-\frac{3mn}{m+n}=\frac{2011}{3}.
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