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2020 BMT Fall
24
2020 BMT Individual 24
2020 BMT Individual 24
Source:
January 9, 2022
number theory
Problem Statement
Let
N
N
N
be the number of non-empty subsets
T
T
T
of
S
=
{
1
,
2
,
3
,
4
,
.
.
.
,
2020
}
S = \{1, 2, 3, 4, . . . , 2020\}
S
=
{
1
,
2
,
3
,
4
,
...
,
2020
}
satisfying
max
(
T
)
>
1000
\max (T) >1000
max
(
T
)
>
1000
. Compute the largest integer
k
k
k
such that
3
k
3^k
3
k
divides
N
N
N
.
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