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Putnam
2019 Putnam
A4
A4
Part of
2019 Putnam
Problems
(1)
Putnam 2019 A4
Source:
12/10/2019
Let
f
f
f
be a continuous real-valued function on
R
3
\mathbb R^3
R
3
. Suppose that for every sphere
S
S
S
of radius
1
1
1
, the integral of
f
(
x
,
y
,
z
)
f(x,y,z)
f
(
x
,
y
,
z
)
over the surface of
S
S
S
equals zero. Must
f
(
x
,
y
,
z
)
f(x,y,z)
f
(
x
,
y
,
z
)
be identically zero?
Putnam
Putnam 2019