Type: Article

On the Fixed Points of the Map x bar right arrow x(x) Modulo a Prime

Kurlberg, Par; Luca, Florian; Shparlinski, Igor E.;

Abstract:

In this paper, we show that for almost all primes p there is an integer solution x is an element of [2, p -1] to the congruence x(x) equivalent to x (mod p). The solutions can be interpretated as fixed points of the map x bar right arrow x(x) (mod p), and we study numerically and discuss some unexpected properties of the dynamical system associated with this map.