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Three coprime roots of an equation

Source: 2022 Israel National Olympiad P4

December 16, 2022
number theoryDiophantine equation

Problem Statement

Find all triples (a,b,c)(a,b,c) of integers for which the equation x3−a2x2+b2x−ab+3c=0x^3-a^2x^2+b^2x-ab+3c=0 has three distinct integer roots x1,x2,x3x_1,x_2,x_3 which are pairwise coprime.
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