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2019-IMOC
A5
f^{x+1}(y)+f^{y+1}(x)=2f(x+y)
f^{x+1}(y)+f^{y+1}(x)=2f(x+y)
Source: IMOC 2019 A5
September 15, 2020
functional equation
Positive integer FE
iterated FE
algebra
IMOC
Problem Statement
Find all functions
f
:
N
↦
N
f : \mathbb N \mapsto \mathbb N
f
:
N
↦
N
such that the following identity
f
x
+
1
(
y
)
+
f
y
+
1
(
x
)
=
2
f
(
x
+
y
)
f^{x+1}(y)+f^{y+1}(x)=2f(x+y)
f
x
+
1
(
y
)
+
f
y
+
1
(
x
)
=
2
f
(
x
+
y
)
holds for all
x
,
y
∈
N
x,y \in \mathbb N
x
,
y
∈
N
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