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2018-IMOC
N1
iterated divisibility FE
iterated divisibility FE
Source: IMOC 2018 N1
August 17, 2021
fe
functional equation
number theory
Problem Statement
Find all functions
f
:
N
→
N
f:\mathbb N\to\mathbb N
f
:
N
→
N
satisfying
x
+
f
f
(
x
)
(
y
)
∣
2
(
x
+
y
)
x+f^{f(x)}(y)\mid2(x+y)
x
+
f
f
(
x
)
(
y
)
∣
2
(
x
+
y
)
for all
x
,
y
∈
N
x,y\in\mathbb N
x
,
y
∈
N
.
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