Short Cycles in Repeated Exponentiation Modulo a Prime

Lev Glebsky, Igor E. Shparlinski

Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u\mapsto f_g(u)$, where $f_g(u)\equiv g^u(\mathrm{mod}p)$ and…