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Mathematics
Problem
Let
w
≠
1
w \neq 1
w
=
1
be a cube root of unity. Then, the minimum of the set
{
∣
a
+
b
ω
+
c
ω
2
∣
2
∣
a
,
b
,
c
distinct non-zero integers
}
\{|a + b\omega + c\omega^2|^2 \mid a, b, c \text{ distinct non-zero integers}\}
{
∣
a
+
bω
+
c
ω
2
∣
2
∣
a
,
b
,
c
distinct non-zero integers
}
equals ---
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