NON-WIEFERICH PRIMES IN ARITHMETIC PROGRESSIONS

作者:Chen, Yong-Gao*; Ding, Yu
来源:PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145(5): 1833-1836.
DOI:10.1090/proc/13201

摘要

Graves and Murty proved that for any integer a >= 2 and any fixed integer k >= 2, there are >> log x/log log x primes p <= x such that a(p-1) not equivalent to 1 (mod p(2)) and p equivalent to 1 (mod k), under the assumption of the abc conjecture. In this paper, for any fixed M, the bound log x/log log x is improved to (log x/log log x)(log log log x)(M).