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Putnam 2019 A4

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December 10, 2019
PutnamPutnam 2019

Problem Statement

Let ff be a continuous real-valued function on R3\mathbb R^3.  Suppose that for every sphere SS of radius 11, the integral of f(x,y,z)f(x,y,z) over the surface of SS equals zero.  Must f(x,y,z)f(x,y,z) be identically zero?
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