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National and Regional Contests
Argentina Contests
Argentina Cono Sur TST
2024 Argentina Cono Sur TST
Problem 2
Problem 2
Part of
2024 Argentina Cono Sur TST
Problems
(1)
Divisibility on 101 integers
Source: Argentina Cono Sur TST 2024 P2
8/9/2024
There are
101
101
101
positive integers
a
1
,
a
2
,
…
,
a
101
a_1, a_2, \ldots, a_{101}
a
1
,
a
2
,
…
,
a
101
such that for every index
i
i
i
, with
1
≤
i
≤
101
1 \leq i \leq 101
1
≤
i
≤
101
,
a
i
+
1
a_i+1
a
i
+
1
is a multiple of
a
i
+
1
a_{i+1}
a
i
+
1
. Find the greatest possible value of the largest of the
101
101
101
numbers.
number theory