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1/2(a^4 +b^4 +c^4) is pefrect square if a+b+c = 0

Source: Flanders Math Olympiad 2008 p2

December 24, 2022
number theoryPerfect Square

Problem Statement

Let a,ba, b and cc be integers such that a+b+c=0a+b+c = 0. Prove that 12(a4+b4+c4)\frac12(a^4 +b^4 +c^4) is a perfect square.
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