On the Golomb’s conjecture and Lehmer’s numbers

• Autorzy: Wang Tingting , Wang Xiaonan
• Języki publikacji: EN

Abstrakty

EN

Let p be an odd prime. For each integer a with 1 ≤ a ≤ p − 1, it is clear that there exists one and only one ā with 1 ≤ ā ≤ p − 1 such that a · ā ≡ 1 mod p. Let N(p) denote the set of all primitive roots a mod p with 1 ≤ a ≤ p − 1 in which a and ā are of opposite parity. The main purpose of this paper is using the analytic method and the estimate for the hybrid exponential sums to study the solvability of the congruence a + b ≡ 1 mod p with a, b ∈ N(p), and give a sharper asymptotic formula for the number of the solutions of the congruence equation.

Słowa kluczowe

EN

D. H. Lehmer’s numbers; Golomb’s conjecture; The hybrid exponential sums; Congruence equation; Primitive roots

Kategorie tematyczne

• 11L03: Trigonometric and exponential sums, general
• 11L07: Estimates on exponential sums

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1003-1009

Daty

wydano

2017-01-01

otrzymano

2016-09-02

zaakceptowano

2017-06-13

online

2017-07-21

Twórcy

autor

Wang Tingting

• , , ,

autor

Wang Xiaonan

• , , ,

Identyfikatory

DOI

10.1515/math-2017-0083