Algebra · Polynomial identities · Symmetric expressions · Power sums
Problem 1, 1997
Let \(a, b, c, d\) be numbers satisfying
\[ a^2 + b^2 + (a+b)^2 = c^2 + d^2 + (c+d)^2 . \]
Prove that then
\[ a^4 + b^4 + (a+b)^4 = c^4 + d^4 + (c+d)^4 . \]
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Serbian Regional Competition (Okruzno takmicenje) 1997, high school grade I, problem 1. The 1997 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).