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quadratic equation with integer root

Source: Czech and Slovak third round,2006,p2

March 3, 2012
quadraticsalgebra unsolvedalgebra

Problem Statement

Let m,nm,n be positive integers such that the equation (in respect of xx) (x+m)(x+n)=x+m+n(x+m)(x+n)=x+m+n has at least one integer root. Prove that 12n<m<2n\frac{1}{2}n<m<2n.
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