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National and Regional Contests
Taiwan Contests
TST Round 2
2021 Taiwan TST Round 2
N
N
Part of
2021 Taiwan TST Round 2
Problems
(1)
Interesting NT Problem That Looks Like 2020 IMO P5
Source: 2021 Taiwan TST Round 2 Independent Study 1-N
4/7/2021
Let
S
S
S
be a set of positive integers such that for every
a
,
b
∈
S
a,b\in S
a
,
b
∈
S
, there always exists
c
∈
S
c\in S
c
∈
S
such that
c
2
c^2
c
2
divides
a
(
a
+
b
)
a(a+b)
a
(
a
+
b
)
. Show that there exists an
a
∈
S
a\in S
a
∈
S
such that
a
a
a
divides every element of
S
S
S
.Proposed by usjl
number theory
Taiwan