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IMO ShortList 1999, number theory problem 2

Source: IMO ShortList 1999, number theory problem 2

November 13, 2004

rationumber theoryrepresentationIMO Shortlist

Problem Statement

Prove that every positive rational number can be represented in the form

\dfrac{a^{3}+b^{3}}{c^{3}+d^{3}}

where a,b,c,d are positive integers.