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IMO Shortlist
2018 IMO Shortlist
A5
A5
Part of
2018 IMO Shortlist
Problems
(1)
Fractions in an FE taking positive reals
Source: IMO Shortlist 2018 A5 (proposed by South Korea)
7/17/2019
Determine all functions
f
:
(
0
,
∞
)
→
R
f:(0,\infty)\to\mathbb{R}
f
:
(
0
,
∞
)
→
R
satisfying
(
x
+
1
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
y
x
)
\left(x+\frac{1}{x}\right)f(y)=f(xy)+f\left(\frac{y}{x}\right)
(
x
+
x
1
)
f
(
y
)
=
f
(
x
y
)
+
f
(
x
y
)
for all
x
,
y
>
0
x,y>0
x
,
y
>
0
.
function
algebra
IMO Shortlist