Estimates for Wieferich numbers

@article{Banks2007EstimatesFW,
  title={Estimates for Wieferich numbers},
  author={W. Banks and F. Luca and I. Shparlinski},
  journal={The Ramanujan Journal},
  year={2007},
  volume={14},
  pages={361-378}
}
  • W. Banks, F. Luca, I. Shparlinski
  • Published 2007
  • Mathematics
  • The Ramanujan Journal
  • Abstract We define Wieferich numbers to be those odd integers w≥3 that satisfy the congruence 2φ(w)≡1 (mod  w2). It is clear that the distribution of Wieferich numbers is closely related to the distribution of Wieferich primes, and we give some quantitative forms of this statement. We establish several unconditional asymptotic results about Wieferich numbers; analogous results for the set of Wieferich primes remain out of reach. Finally, we consider several modifications of the above definition… CONTINUE READING
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