TY - JOUR

T1 - Pseudorandomness and dynamics of fermat quotients*

AU - Ostafe, Alina

AU - Shparlinski, Igor E.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79956119865&partnerID=8YFLogxK

U2 - 10.1137/100798466

DO - 10.1137/100798466

M3 - Article

VL - 25

SP - 50

EP - 71

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 1

ER -