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13
Math Prize 2012 Problem 13
Math Prize 2012 Problem 13
Source:
September 24, 2012
complex numbers
Problem Statement
For how many integers
n
n
n
with
1
≤
n
≤
2012
1 \le n \le 2012
1
≤
n
≤
2012
is the product
∏
k
=
0
n
−
1
(
(
1
+
e
2
π
i
k
/
n
)
n
+
1
)
\prod_{k=0}^{n-1} \left( \left( 1 + e^{2 \pi i k / n} \right)^n + 1 \right)
k
=
0
∏
n
−
1
(
(
1
+
e
2
πik
/
n
)
n
+
1
)
equal to zero?
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