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Putnam
2023 Putnam
B2
B2
Part of
2023 Putnam
Problems
(1)
2023 Putnam B2
Source:
12/3/2023
For each positive integer
n
n
n
, let
k
(
n
)
k(n)
k
(
n
)
be the number of ones in the binary representation of
2023
ā
n
2023 \cdot n
2023
ā
n
. What is the minimum value of
k
(
n
)
k(n)
k
(
n
)
?
Putnam
Putnam 2023