PRIMES p ≡ 1 mod d AND a(p1)/d ≡ 1 mod p

Peng Gao; Liangyi Zhao

PRIMES p ≡ 1 mod d AND a^(p1)/d ≡ 1 mod p

Peng Gao
, Liangyi Zhao

School of Mathematical Sciences

University of New South Wales

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose that d ∈ {2, 3, 4, 6} and a ∈ Z with a≠ -1 and a is not square. Let P_(a,d) be the number of primes p not exceeding x such that p ≡ 1 (mod d) and a^(p-1)/d ≡ 1 (mod p). In this paper, we study the mean value of P_(a,d).

Original language	English
Article number	A33
Journal	Integers
Volume	19
State	Published - 2019

Cite this

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title = "PRIMES p ≡ 1 mod d AND a(p1)/d ≡ 1 mod p",

abstract = "Suppose that d ∈ \{2, 3, 4, 6\} and a ∈ Z with a≠ -1 and a is not square. Let P(a,d) be the number of primes p not exceeding x such that p ≡ 1 (mod d) and a(p-1)/d ≡ 1 (mod p). In this paper, we study the mean value of P(a,d).",

author = "Peng Gao and Liangyi Zhao",

year = "2019",

language = "英语",

volume = "19",

journal = "Integers",

issn = "1553-1732",

publisher = "Colgate University",

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TY - JOUR

T1 - PRIMES p ≡ 1 mod d AND a(p1)/d ≡ 1 mod p

AU - Gao, Peng

AU - Zhao, Liangyi

PY - 2019

Y1 - 2019

N2 - Suppose that d ∈ {2, 3, 4, 6} and a ∈ Z with a≠ -1 and a is not square. Let P(a,d) be the number of primes p not exceeding x such that p ≡ 1 (mod d) and a(p-1)/d ≡ 1 (mod p). In this paper, we study the mean value of P(a,d).

AB - Suppose that d ∈ {2, 3, 4, 6} and a ∈ Z with a≠ -1 and a is not square. Let P(a,d) be the number of primes p not exceeding x such that p ≡ 1 (mod d) and a(p-1)/d ≡ 1 (mod p). In this paper, we study the mean value of P(a,d).

UR - https://www.scopus.com/pages/publications/85152790443

M3 - 文章

AN - SCOPUS:85152790443

SN - 1553-1732

VL - 19

JO - Integers

JF - Integers

M1 - A33

ER -

PRIMES p ≡ 1 mod d AND a(p1)/d ≡ 1 mod p

Abstract

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PRIMES p ≡ 1 mod d AND a^(p1)/d ≡ 1 mod p