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COUNTING FIXED POINTS, TWO-CYCLES, AND COLLISIONS OF THE DISCRETE EXPONENTIAL FUNCTION USING p-ADIC METHODS

  • JOSHUA HOLDEN (a1) and MARGARET M. ROBINSON (a2)
Abstract
Abstract

Brizolis asked for which primes p greater than 3 there exists a pair (g,h) such that h is a fixed point of the discrete exponential map with base g, or equivalently h is a fixed point of the discrete logarithm with base g. Various authors have contributed to the understanding of this problem. In this paper, we use p-adic methods, primarily Hensel’s lemma and p-adic interpolation, to count fixed points, two-cycles, collisions, and solutions to related equations modulo powers of a prime p.

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Copyright
Corresponding author
For correspondence; e-mail: robinson@mtholyoke.edu
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The first-named author thanks the Hutchcroft Fund at Mount Holyoke College for support.

Footnotes
References
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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