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Math Prize For Girls Problems
2023 Math Prize for Girls Problems
19
19
Part of
2023 Math Prize for Girls Problems
Problems
(1)
Math Prize 2023 Problem 19
Source:
10/12/2023
Let
N
=
∏
k
=
1
1000
(
4
k
−
1
)
\displaystyle{N = \prod_{k=1}^{1000} (4^k - 1)}
N
=
k
=
1
∏
1000
(
4
k
−
1
)
. Determine the largest positive integer
n
n
n
such that
5
n
5^n
5
n
divides evenly into
N
N
N
.