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Taiwan Contests
TST Round 3
2018 Taiwan TST Round 3
5
Functional equation 012
Functional equation 012
Source: 2018 Taiwan TST Round 3, Day 5, Problem 2
April 28, 2018
algebra
functional equation
function
Taiwan
Problem Statement
Find all functions
f
:
N
→
N
f: \mathbb{N} \to \mathbb{N}
f
:
N
→
N
such that
f
(
x
+
y
f
(
x
)
)
=
x
+
f
(
y
)
f
(
x
)
f\left(x+yf\left(x\right)\right) = x+f\left(y\right)f\left(x\right)
f
(
x
+
y
f
(
x
)
)
=
x
+
f
(
y
)
f
(
x
)
holds for all
x
,
y
∈
N
x,y \in \mathbb{N}
x
,
y
∈
N
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