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Problems
Contests
National and Regional Contests
Ireland Contests
Ireland National Math Olympiad
2022 Irish Math Olympiad
4
4
Part of
2022 Irish Math Olympiad
Problems
(1)
finding a given value of a function
Source: IrMO 2022
5/8/2022
4. Let
N
\mathbb{N}
N
denote the strictly positive integers. A function
f
f
f
:
N
\mathbb{N}
N
→
\to
→
N
\mathbb{N}
N
has the following properties which hold for all
n
∈
n \in
n
∈
N
\mathbb{N}
N
:a)
f
(
n
)
f(n)
f
(
n
)
<
f
(
n
+
1
)
f(n+1)
f
(
n
+
1
)
; b)
f
(
f
(
f
(
n
)
)
)
f(f(f(n)))
f
(
f
(
f
(
n
)))
= 4
n
n
n
Find
f
(
2022
)
f(2022)
f
(
2022
)
.
function
algebra