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5.3
2018 PUMaC Live Round 5.3
2018 PUMaC Live Round 5.3
Source:
January 13, 2019
PuMAC
Live Round
Problem Statement
Let
k
k
k
be the largest integer such that
2
k
2^k
2
k
divides
(
∏
n
=
1
25
(
∑
i
=
0
n
(
n
i
)
)
2
)
(
∏
n
=
1
25
(
∑
i
=
0
n
(
n
i
)
2
)
)
.
\left(\prod_{n=1}^{25}\left(\sum_{i=0}^n\binom{n}{i}\right)^2\right)\left(\prod_{n=1}^{25}\left(\sum_{i=0}^n\binom{n}{i}^2\right)\right).
n
=
1
∏
25
(
i
=
0
∑
n
(
i
n
)
)
2
(
n
=
1
∏
25
(
i
=
0
∑
n
(
i
n
)
2
)
)
.
Find
k
k
k
.
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