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Canadian Mathematical Olympiad Qualification Repechage
2024 Canadian Mathematical Olympiad Qualification
1
f(x + f(xy)) = f(x)(1 + y)
f(x + f(xy)) = f(x)(1 + y)
Source: Canada Repêchage 2024/1 CMOQR
March 25, 2024
algebra
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f : R \to R
f
:
R
ā
R
that satisfy the functional equation
f
(
x
+
f
(
x
y
)
)
=
f
(
x
)
(
1
+
y
)
.
f(x + f(xy)) = f(x)(1 + y).
f
(
x
+
f
(
x
y
))
=
f
(
x
)
(
1
+
y
)
.
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