CORE
πΊπ¦Β
Β make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
Filters
194,121 research outputs found
Primes
p
β‘
1
β
m
o
d
β
d
p \equiv 1 \bmod{d}
p
β‘
1
mod
d
and
a
(
p
β
1
)
/
d
β‘
1
β
m
o
d
β
p
a^{(p-1)/d} \equiv 1 \bmod{p}
a
(
p
β
1
)
/
d
β‘
1
mod
p
}
Author
Gao Peng
Zhao Liangyi
Publication venue
Publication date
22/03/2019
Field of study
Full text link
Suppose that
d
β
{
2
,
3
,
4
,
6
}
d \in \{ 2, 3, 4, 6 \}
d
β
{
2
,
3
,
4
,
6
}
and
a
β
Z
a \in \mathbb{Z}
a
β
Z
with
a
β
β
1
a\neq -1
a
ξ
=
β
1
and
a
a
a
is not square. Let
P
(
a
,
d
)
P_{(a,d)}
P
(
a
,
d
)
β
be the number of primes
p
p
p
not exceeding
x
x
x
such that
p
β‘
1
(
m
o
d
d
)
p \equiv 1 \pmod{d}
p
β‘
1
(
mod
d
)
and
a
(
p
β
1
)
/
d
β‘
1
(
m
o
d
p
)
a^{(p-1)/d} \equiv 1 \pmod{p}
a
(
p
β
1
)
/
d
β‘
1
(
mod
p
)
. In this paper, we study the mean value of
P
(
a
,
d
)
P_{(a,d)}
P
(
a
,
d
)
β
.Comment: 8 page
arXiv.org e-Print Archive
UNSWorks
1
2
3
β¦
last