ON SEMIGROUP ORBITS OF POLYNOMIALS AND MULTIPLICATIVE ORDERS
JORGE MELLO · Bulletin of the Australian Mathematical Society · 2020
We show, under some natural restrictions, that some semigroup orbits of polynomials cannot contain too many elements of small multiplicative order modulo a large prime $p$ , extending previous work of Shparlinski [‘Multiplicative orders in orbits of polynomials over finite fields’, Glasg. Math. J.60(2) (2018), 487–493].