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Switzerland Team Selection Test
2020 Switzerland Team Selection Test
2
2
Part of
2020 Switzerland Team Selection Test
Problems
(1)
Cute nt from Switzerland
Source: Swiss IMO TST 2020 P2
9/28/2021
Find all positive integers
n
n
n
such that there exists an infinite set
A
A
A
of positive integers with the following property: For all pairwise distinct numbers
a
1
,
a
2
,
…
,
a
n
∈
A
a_1, a_2, \ldots , a_n \in A
a
1
,
a
2
,
…
,
a
n
∈
A
, the numbers
a
1
+
a
2
+
…
+
a
n
and
a
1
⋅
a
2
⋅
…
⋅
a
n
a_1 + a_2 + \ldots + a_n \text{ and } a_1\cdot a_2\cdot \ldots\cdot a_n
a
1
+
a
2
+
…
+
a
n
and
a
1
⋅
a
2
⋅
…
⋅
a
n
are coprime.
number theory
coprime