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\frac{a+b}{a^2+k^2b^2-k^2ab} is a composite number for all a,b \in N+

Source: Greek National 2020 p4 (Archimedes)

February 23, 2020
composite numberpositive integersnumber theoryComposite

Problem Statement

Find all values of the positive integer kk that has the property: There are no positive integers a,ba,b such that the expression A(k,a,b)=a+ba2+k2b2−k2abA(k,a,b)=\frac{a+b}{a^2+k^2b^2-k^2ab} is a composite positive number.
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