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Baltic Way
2021 Baltic Way
1
1
Part of
2021 Baltic Way
Problems
(1)
fe with natural on reals
Source: Baltic Way 2021, Problem 1
11/15/2021
Let
n
n
n
be a positive integer. Find all functions
f
:
R
→
R
f\colon \mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
that satisfy the equation
(
f
(
x
)
)
n
f
(
x
+
y
)
=
(
f
(
x
)
)
n
+
1
+
x
n
f
(
y
)
(f(x))^n f(x+y) = (f(x))^{n+1} + x^n f(y)
(
f
(
x
)
)
n
f
(
x
+
y
)
=
(
f
(
x
)
)
n
+
1
+
x
n
f
(
y
)
for all
x
,
y
∈
R
x ,y \in \mathbb{R}
x
,
y
∈
R
.
algebra
algebra proposed
functional equation