Primes $p \equiv 1 \bmod{d}$ and $a^{(p-1)/d} \equiv 1 \bmod{p}$}

Peng Gao; Liangyi Zhao

paper

Primes $p \equiv 1 mod d$ and $a^{(p - 1) / d} \equiv 1 mod p$ }

arXiv:1807.09410

Abstract

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

8 pages

References in corpus (1)

Mean values with cubic characters

Primes p≡1modd and a(p−1)/d≡1modp}

Abstract

References in corpus (1)

Primes $p \equiv 1 mod d$ and $a^{(p - 1) / d} \equiv 1 mod p$ }