Let f be a continuous real-valued function on R3. Suppose that for every sphere S of radius 1, the integral of f(x, y, z) over the surface of S equals 0. Must f(x, y, z) = 0 for all points (x, y, z)?
Let f be a continuous real-valued function on R3. Suppose that for every sphere S of radius 1, the integral of f(x, y, z) over the surface of S equals 0. Must f(x, y, z) = 0 for all points (x, y, z)?
It's a question from a math competition, so if you'd answered it then you would get something