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Strange algebraic geometry

Source: Tournament of Towns 2020 Senior A-level

October 25, 2020
geometryalgebrapolynomialVietaTournament of TownsToTBaron Munchausen

Problem Statement

Baron Munchausen presented a new theorem: if a polynomial xn−axn−1+bxn−2+…x^{n} - ax^{n-1} + bx^{n-2}+ \dots has nn positive integer roots then there exist aa lines in the plane such that they have exactly bb intersection points. Is the baron’s theorem true?
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