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National and Regional Contests
China Contests
(China) National High School Mathematics League
2011 China Second Round Olympiad
8
integers in the sequence
integers in the sequence
Source: China Second Round Test1
January 30, 2012
number theory unsolved
number theory
Problem Statement
Given that
a
n
=
(
200
n
)
⋅
6
200
−
n
3
⋅
(
1
2
)
n
a_{n}= \binom{200}{n} \cdot 6^{\frac{200-n}{3}} \cdot (\dfrac{1}{\sqrt{2}})^n
a
n
=
(
n
200
)
⋅
6
3
200
−
n
⋅
(
2
1
)
n
(
1
≤
n
≤
95
1 \leq n \leq 95
1
≤
n
≤
95
). How many integers are there in the sequence
{
a
n
}
\{a_n\}
{
a
n
}
?
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