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Cono Sur Olympiad 2012

Source: Problem 3

November 3, 2012
symmetrynumber theoryrelatively primenumber theory proposed

Problem Statement

3. Show that there do not exist positive integers aa, bb, cc and dd, pairwise co-prime, such that ab+cdab+cd, ac+bdac+bd and ad+bcad+bc are odd divisors of the number (a+b−c−d)(a−b+c−d)(a−b−c+d)(a+b-c-d)(a-b+c-d)(a-b-c+d).
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