Let $S$ be an equilateral triangle, and $f$ is a continuous function such that for any point $O$ inside $S$, with distances $x,y,z$ from vertices of $S$, $f(x)+f(y)+f(z)=0$. Prove that $f$ is identically zero.
2026-04-01 01:33:30.1775007210
continuous function in a triangle
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