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a^2|(b^3+c^3), b^2|(a^3+c^3), c^2|(a^3+b^3)

Source: SMO 2011 Problem 2

August 18, 2011
number theorygreatest common divisornumber theory unsolved

Problem Statement

If positive integers, a,b,ca,b,c are pair-wise co-prime, and,  a2(b3+c3),b2(a3+c3),c2(a3+b3)\ a^2|(b^3+c^3), b^2|(a^3+c^3), c^2|(a^3+b^3) find a,b,a,b, and cc