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Set S of positive reals

Source: Saudi Arabia IMO TST Day II Problem 2

July 22, 2014
algebra unsolvedalgebra

Problem Statement

Let SS be a set of positive real numbers with five elements such that for any distinct a, b, ca,~ b,~ c in SS, the number ab+bc+caab + bc + ca is rational. Prove that for any aa and bb in SS, ab\tfrac{a}{b} is a rational number.
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