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
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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.

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Cite this paper

APA

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

Chicago

Witno, Amin. “Modular Zero Divisors of Longest Exponentiation Cycle.” Notes on Number Theory and Discrete Mathematics 19, no. 3 (2013): 66-69.

MLA

Witno, Amin. “Modular Zero Divisors of Longest Exponentiation Cycle.” Notes on Number Theory and Discrete Mathematics 19.3 (2013): 66-69. Print.

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