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1995 Moldova Team Selection Test
1
$\sum_{k=1}^{n} cos^{2m} \frac{k\pi}{2n+1}$
$\sum_{k=1}^{n} cos^{2m} \frac{k\pi}{2n+1}$
Source: Moldova TST 1995
August 8, 2023
trigonometry
Problem Statement
Prove that for any positive integers
m
m{}
m
and
n
n{}
n
the number
∑
k
=
1
n
c
o
s
2
m
k
π
2
n
+
1
\sum_{k=1}^{n} cos^{2m} \frac{k\pi}{2n+1}
∑
k
=
1
n
co
s
2
m
2
n
+
1
kπ
is not an integer.
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