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2023 JBMO Shortlist
N5
N5
Part of
2023 JBMO Shortlist
Problems
(1)
JBMO Shortlist 2023 N5
Source: JBMO Shortlist 2023, N5
6/28/2024
Find the largest positive integer
k
k
k
such that we can find a set
A
⊆
{
1
,
2
,
…
,
100
}
A \subseteq \{1,2, \ldots, 100 \}
A
⊆
{
1
,
2
,
…
,
100
}
with
k
k
k
elements such that, for any
a
,
b
∈
A
a,b \in A
a
,
b
∈
A
,
a
a
a
divides
b
b
b
if and only if
s
(
a
)
s(a)
s
(
a
)
divides
s
(
b
)
s(b)
s
(
b
)
, where
s
(
k
)
s(k)
s
(
k
)
denotes the sum of the digits of
k
k
k
.
JBMO
JBMO Shortlist
number theory