NON-WIEFERICH PRIMES IN ARITHMETIC PROGRESSIONS.

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 ap-1 ≢ 1 (mod p2) and p ≡ 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. [ABSTRACT FROM AUTHOR]