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National and Regional Contests
North Macedonia Contests
Macedonian Team Selection Test
2023 Macedonian Team Selection Test
Problem 3
Problem 3
Part of
2023 Macedonian Team Selection Test
Problems
(1)
Maximal value of 2023 under monotonic function
Source: 2023 Macedonian Team Selection Test P3
5/21/2023
Let
f
:
N
ā
N
f:\mathbb{N} \rightarrow \mathbb{N}
f
:
N
ā
N
be a monotonically increasing function over the natural numbers, such that
f
(
f
(
n
)
)
=
n
2
f(f(n))=n^{2}
f
(
f
(
n
))
=
n
2
. What is the smallest, and what is the largest value that
f
(
2023
)
f(2023)
f
(
2023
)
can take?Proposed by Ilija Jovcheski
function
algebra