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2020 IMO Shortlist
A8
A8
Part of
2020 IMO Shortlist
Problems
(1)
Hard functional equation
Source: IMO shortlist A8 2020
7/20/2021
Let
R
+
R^+
R
+
be the set of positive real numbers. Determine all functions
f
:
R
+
f:R^+
f
:
R
+
ā
\rightarrow
ā
R
+
R^+
R
+
such that for all positive real numbers
x
x
x
and
y
:
y:
y
:
f
(
x
+
f
(
x
y
)
)
+
y
=
f
(
x
)
f
(
y
)
+
1
f(x+f(xy))+y=f(x)f(y)+1
f
(
x
+
f
(
x
y
))
+
y
=
f
(
x
)
f
(
y
)
+
1
Ukraine
functional equation
algebra
IMO Shortlist