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5
2023 LMT Spring Accuracy Problem 5
2023 LMT Spring Accuracy Problem 5
Source:
September 29, 2023
number theory
Problem Statement
Let
N
=
∑
i
=
0
512
i
(
512
i
)
.
N = \sum^{512}_{i=0}i {512 \choose i}.
N
=
i
=
0
∑
512
i
(
i
512
)
.
What is the greatest integer
a
a
a
such that
2
a
2^a
2
a
is a divisor of
N
N
N
?
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