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Romanian Masters of Mathematics Collection
2019 Romanian Master of Mathematics
5
Functional equation wrapped in f's
Functional equation wrapped in f's
Source: RMM 2019 Problem 5
February 24, 2019
algebra
functional equation
functions
Problem Statement
Determine all functions
f
:
R
ā
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
satisfying
f
(
x
+
y
f
(
x
)
)
+
f
(
x
y
)
=
f
(
x
)
+
f
(
2019
y
)
,
f(x + yf(x)) + f(xy) = f(x) + f(2019y),
f
(
x
+
y
f
(
x
))
+
f
(
x
y
)
=
f
(
x
)
+
f
(
2019
y
)
,
for all real numbers
x
x
x
and
y
y
y
.
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