Modular zero divisors of longest exponentiation cycle

Amin Witno
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 3, Pages 66–69
Full paper (PDF, 115 Kb)

Details

Authors and affiliations

Amin Witno
Department of Basic Sciences
Philadelphia University, 19392 Jordan

Abstract

We show that the sequence wk mod n, given that gcd(w, n) > 1, can reach a maximal cycle length of ϕ(n) if and only if n is twice an odd prime power, w is even, and w is a primitive root modulo n=2.

Keywords

  • Modular exponentiation
  • Primitive roots

AMS Classification

  • 11A05
  • 11A07

References

  1. Dummit, D. S., R. M. Foote, Abstract Algebra, 3rd ed., Wiley, 2003.
  2. Witno, A. Theory of Numbers, BookSurge Publishing, 2008.

Related papers

Cite this paper

Witno, A. (2013). Modular zero divisors of longest exponentiation cycle. Notes on Number Theory and Discrete Mathematics, 19(3), 66-69.

Comments are closed.