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IMO Longlists
1987 IMO Longlists
73
73
Part of
1987 IMO Longlists
Problems
(1)
IMO LongList 1987 - Prove that there exist x, y
Source:
9/6/2010
Let
f
(
x
)
f(x)
f
(
x
)
be a periodic function of period
T
>
0
T > 0
T
>
0
defined over
R
\mathbb R
R
. Its first derivative is continuous on
R
\mathbb R
R
. Prove that there exist
x
,
y
∈
[
0
,
T
)
x, y \in [0, T )
x
,
y
∈
[
0
,
T
)
such that
x
≠
y
x \neq y
x
=
y
and
f
(
x
)
f
′
(
y
)
=
f
′
(
x
)
f
(
y
)
.
f(x)f'(y)=f'(x)f(y).
f
(
x
)
f
′
(
y
)
=
f
′
(
x
)
f
(
y
)
.
function
calculus
derivative
algebra proposed
algebra