A problem of D. H. Lehmer and its mean value

✍ Scribed by Zhefeng Xu; Wenpeng Zhang

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 135 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510628

✦ Synopsis

Abstract

Let p be an odd prime and let a be an integer coprime to p. Denote by N (a, p) the number of pairs of integers b, c with bc ≡ a (mod p), 1 ≤ b, c < p and with b, c having different parity. The main purpose of this paper is to deduce an asymptotic formula for (N (2__^s^ad__, p) – 1/2 (p – 1)), and obtain some interesting results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)