# Properties of the Graph Arising from Certain Map over a Finite Field

## Annual Meeting in Mathematics 2023

## Keywords:

graph of iteration, finite field, cycle, tail## Abstract

For primes $p$ and $q$, the graph obtained from iterating the map $x \mapsto x^p$ over the finite field of $q^2$ elements is considered. Asymptotic formulas for the sum, over bounded primes $q$, of the total number of elements in all cycles and that of all tail lengths are derived.

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## How to Cite

*Thai Journal of Mathematics*,

*22*(1), 251–262. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1614