Pseudorandomness and dynamics of fermat quotients*

Alina Ostafe*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

61 Citations (Scopus)


We obtain some theoretical and experimental results concerning various properties (the number of fixed points, image distribution, cycle lengths) of the dynamical system naturally associated with Fermat quotients acting on the set {0, ⋯ , p - 1}. In particular, we improve the lower bound of Vandiver [Bull. Amer. Math. Soc., 22 (1915), pp. 61-67] on the image size of Fermat quotients on the above set (from p1/2 - 1 to (1+o(1))p(log p) -2). We also consider pseudorandom properties of Fermat quotients such as uniform distribution and linear complexity.

Original languageEnglish
Pages (from-to)50-71
Number of pages22
JournalSIAM Journal on Discrete Mathematics
Issue number1
Publication statusPublished - 2011


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