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2023 AIME
8
bashing out 3^7 terms
bashing out 3^7 terms
Source: 2023 AIME II/8
February 16, 2023
AMC
AIME
AIME II
Problem Statement
Let
ω
=
cos
2
π
7
+
i
⋅
sin
2
π
7
\omega=\cos\frac{2\pi}{7}+i\cdot\sin\frac{2\pi}{7}
ω
=
cos
7
2
π
+
i
⋅
sin
7
2
π
, where
i
=
−
1
i=\sqrt{-1}
i
=
−
1
. Find
∏
k
=
0
6
(
ω
3
k
+
ω
k
+
1
)
.
\prod_{k=0}^{6}(\omega^{3k}+\omega^k+1).
k
=
0
∏
6
(
ω
3
k
+
ω
k
+
1
)
.
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