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2024 Iberoamerican
6
6
Part of
2024 Iberoamerican
Problems
(1)
Infinite set with a curious propety
Source: Iberoamerican MO 2024 Day 2 P6
9/23/2024
Determine all infinite sets
A
A
A
of positive integers with the following propety: If
a
,
b
∈
A
a,b \in A
a
,
b
∈
A
and
a
≥
b
a \ge b
a
≥
b
then
⌊
a
b
⌋
∈
A
\left\lfloor \frac{a}{b} \right\rfloor \in A
⌊
b
a
⌋
∈
A
number theory
floor function