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Putnam
2005 Putnam
B3
Putnam 2005 B3
Putnam 2005 B3
Source:
December 5, 2005
Putnam
function
integration
logarithms
algebra
functional equation
absolute value
Problem Statement
Find all differentiable functions
f
:
(
0
,
∞
)
↦
(
0
,
∞
)
f: (0,\infty)\mapsto (0,\infty)
f
:
(
0
,
∞
)
↦
(
0
,
∞
)
for which there is a positive real number
a
a
a
such that
f
′
(
a
x
)
=
x
f
(
x
)
f'\left(\frac ax\right)=\frac x{f(x)}
f
′
(
x
a
)
=
f
(
x
)
x
for all
x
>
0.
x>0.
x
>
0.
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