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Iran MO (3rd Round)
2005 Iran MO (3rd Round)
2
m=a^2+a+1
m=a^2+a+1
Source: Iran 2005
August 29, 2005
number theory proposed
number theory
Problem Statement
Let
a
∈
N
a\in\mathbb N
a
∈
N
and
m
=
a
2
+
a
+
1
m=a^2+a+1
m
=
a
2
+
a
+
1
. Find the number of
0
≤
x
≤
m
0\leq x\leq m
0
≤
x
≤
m
that:x^3\equiv1(\mbox{mod}\ m)
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