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PEN D Problems
4
4
Part of
PEN D Problems
Problems
(1)
D 4
Source:
5/25/2007
Let
n
n
n
be a positive integer. Prove that
n
n
n
is prime if and only if
(
n
−
1
k
)
≡
(
−
1
)
k
(
m
o
d
n
)
{{n-1}\choose k}\equiv (-1)^{k}\pmod{n}
(
k
n
−
1
)
≡
(
−
1
)
k
(
mod
n
)
for all
k
∈
{
0
,
1
,
⋯
,
n
−
1
}
k \in \{ 0, 1, \cdots, n-1 \}
k
∈
{
0
,
1
,
⋯
,
n
−
1
}
.
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