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2019-IMOC
A4
iterated FE over N
iterated FE over N
Source: IMOC 2019 A4
August 18, 2021
fe
functional equation
algebra
Problem Statement
Find all functions
f
:
N
ā
N
f:\mathbb N\to\mathbb N
f
:
N
ā
N
so that
f
2
f
(
b
)
(
2
a
)
=
f
(
f
(
a
+
b
)
)
+
a
+
b
f^{2f(b)}(2a)=f(f(a+b))+a+b
f
2
f
(
b
)
(
2
a
)
=
f
(
f
(
a
+
b
))
+
a
+
b
holds for all positive integers
a
,
b
a,b
a
,
b
.
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