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2020 Princeton University Math Competition
10
10
Part of
2020 Princeton University Math Competition
Problems
(1)
2020 PUMaC Team 10
Source:
1/1/2022
Let
N
N
N
be the number of sequences of positive integers greater than
1
1
1
where the product of all of the terms of the sequence is
1
2
64
12^{64}
1
2
64
. If
N
N
N
can be expressed as
a
(
2
b
)
a(2^b)
a
(
2
b
)
), where
a
a
a
is an odd positive integer, determine
b
b
b
.
number theory