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Triangle Sides

Source: Baltic Way 2015

November 8, 2015
TriangleSides of a trianglenumber theory

Problem Statement

Three pairwairs distinct positive integers a,b,c,a,b,c, with gcd(a,b,c)=1gcd(a,b,c)=1, satisfy a∣(b−c)2,b∣(a−c)2,c∣(a−b)2a|(b-c)^2 ,b|(a-c)^2 , c|(a-b)^2 Prove that there doesnt exist a non-degenerate triangle with side lengths a,b,c.a,b,c.
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