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Balkan MO
1992 Balkan MO
4
4
Part of
1992 Balkan MO
Problems
(1)
A set in which three elements pairwise coprime exist
Source: Balkan MO 1992, Problem 4
4/25/2006
For each integer
n
≥
3
n\geq 3
n
≥
3
, find the least natural number
f
(
n
)
f(n)
f
(
n
)
having the property
⋆
\star
⋆
For every
A
⊂
{
1
,
2
,
…
,
n
}
A \subset \{1, 2, \ldots, n\}
A
⊂
{
1
,
2
,
…
,
n
}
with
f
(
n
)
f(n)
f
(
n
)
elements, there exist elements
x
,
y
,
z
∈
A
x, y, z \in A
x
,
y
,
z
∈
A
that are pairwise coprime.
number theory proposed
number theory