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abc can be written as a ratio of a cube and square

Source: Bulgarian MO 2003: P5

May 22, 2014
inequalitiesLaTeXnumber theory unsolvednumber theory

Problem Statement

Let a,b,ca,b,c be rational numbers such that a+b+ca+b+c and a2+b2+c2a^2+b^2+c^2 are equal integers. Prove that the number abcabc can be written as the ratio of a perfect cube and a perfect square which are relatively prime.
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