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3
J 3
J 3
Source:
May 25, 2007
modular arithmetic
number theory
greatest common divisor
Divisor Functions
Problem Statement
If
p
p
p
is a prime and
n
n
n
an integer such that
1
<
n
≤
p
1<n \le p
1
<
n
≤
p
, then
ϕ
(
∑
k
=
0
p
−
1
n
k
)
≡
0
(
m
o
d
p
)
.
\phi \left( \sum_{k=0}^{p-1}n^{k}\right) \equiv 0 \; \pmod{p}.
ϕ
(
k
=
0
∑
p
−
1
n
k
)
≡
0
(
mod
p
)
.
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