The graph of the square mapping on the prime fields

✍ Scribed by Thomas D. Rogers

• Book ID: 103060405
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 337 KB
• Volume: 148
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)00250-m

✦ Synopsis

The action of the quadratic map f(x) = x 2 on the multiplicative groups Fp of the prime fields is examined in terms of an associated directed graph that sends an edge from each element to its image. A formula is given for the decomposition of the graph into cyclic components and their attached trees. The number of components c(p) (called the connectivity of the prime p) is shown to take on certain values, assuming various hypotheses.