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2007 Romania National Olympiad
1
complex equation
complex equation
Source: romanian nmo 2007, grade 10, problem 1
April 15, 2007
algebra unsolved
algebra
Problem Statement
Show that the equation
z
n
+
z
+
1
=
0
z^{n}+z+1=0
z
n
+
z
+
1
=
0
has a solution with
∣
z
∣
=
1
|z|=1
∣
z
∣
=
1
if and only if
n
−
2
n-2
n
−
2
is divisble by
3
3
3
.
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