与同余式a^k≡b(modp)相关的迭代图的结构

The Structure of Digraphs Associated with the Congruences a^k≡ b( mod p)

考虑在有限域GF(p)上的同余式ak≡b(modp)构成的图的性质,研究迭代图与整数之间的对应关系,进而给出有限域GF(p)上整数的一个分类。利用每一个顶点都有内度的特点,研究在G(p,k)上的循环和固定点的性质,得到一些有趣的结果,特别地,计算k为奇数时,在迭代图G(p,k)上循环的个数。利用图论的手段研究抽象的数论问题,可以更直观的来分析整数的性质。

we consider the properties of graphs based on iteration of the maps over a finite field. By studying the relationship between graphs and integers,we give a classification of integers over the finite field. We investigate the properties of fixed points and the cycles in by using the characteristics of every vertex having in-degree,and reach some interesting results. In particular,we calculate the number of the cycles in whenis odd. It will be more intuitive to analyze the characteristics of integers through the use of graph theory to study the problems of the abstract number theory.