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Korea National Olympiad
2008 Korean National Olympiad
5
2008 KMO P5
2008 KMO P5
Source:
August 9, 2015
modular arithmetic
number theory
Problem Statement
Let
p
p
p
be a prime where
p
≥
5
p \ge 5
p
≥
5
. Prove that
∃
n
\exists n
∃
n
such that
1
+
(
∑
i
=
2
n
1
i
2
)
(
∏
i
=
2
n
i
2
)
≡
0
(
m
o
d
p
)
1+ (\sum_{i=2}^n \frac{1}{i^2})(\prod_{i=2}^n i^2) \equiv 0 \pmod p
1
+
(
∑
i
=
2
n
i
2
1
)
(
∏
i
=
2
n
i
2
)
≡
0
(
mod
p
)
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