olymmath

Putnam 2019 A4

  • Session A

Let ff be a continuous real-valued function on R3\mathbb{R}^3. Suppose that for every sphere SS of radius 1, the integral of f(x,y,z)f(x,y,z) over the surface of SS equals 0. Must f(x,y,z)f(x,y,z) be identically 0?

Curated text Kedlaya Putnam archive. Quoted with source.

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