Estimates for Wieferich numbers

  title={Estimates for Wieferich numbers},
  author={W. Banks and F. Luca and I. Shparlinski},
  journal={The Ramanujan Journal},
  • 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
    2 Citations
    Pseudorandomness and Dynamics of Fermat Quotients
    • 55
    • PDF
    On the solutions of certain congruences
    • Highly Influenced


    Wieferich's criterion and the abc-conjecture
    • 160
    The continuing search for Wieferich primes
    • 26
    • PDF
    The Prime k-Tuplets Conjecture on Average
    • 37
    A search for Wieferich and Wilson primes
    • 115
    • PDF
    Fermat Quotients for Composite Moduli
    • 40
    • Highly Influential
    • PDF
    Primes in short intervals
    • 41
    On a conjecture of Crandall concerning the qx + 1 problem
    • 22
    • Highly Influential
    • PDF
    On the Normal Behavior of the Iterates Of some Arithmetic Functions
    • 76
    • PDF
    Analytic Number Theory
    • 2,378
    • PDF
    On a problem of Oppenheim concerning “factorisatio numerorum”
    • 311
    • PDF