Balancing non-Wieferich primes in arithmetic progressions View Full Text


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Article Info

DATE

2019-04

AUTHORS

Utkal Keshari Dutta, Bijan Kumar Patel, Prasanta Kumar Ray

ABSTRACT

A prime is called a balancing non-Wieferich prime if it satisfies Bp-8p≢0(modp2), where 8p and Bn denote the Jacobi symbol and the n-th balancing number respectively. For any positive integers k>2 and n>1, there are ≫logx/loglogx balancing non-Wieferich primes p≤x such that p≡1(modk) under the assumption of the abc conjecture for the number field Q(2) (Proc. Japan Acad. Ser. A92 (2016) 112–116). In this paper, for any fixed M, the lower bound logx/loglogx is improved to (logx/loglogx)(logloglogx)M. More... »

PAGES

21

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URI

http://scigraph.springernature.com/pub.10.1007/s12044-018-0459-3

DOI

http://dx.doi.org/10.1007/s12044-018-0459-3

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https://app.dimensions.ai/details/publication/pub.1112141883


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