A discrete iteration in number theory. (Hungarian. English, German summaries) Zbl 0801.11011

Szalay, László

Berzsenyi Dániel Tanárk. Föisk. Tud. Közl., Termtud. 8(3), 71-91 (1992).

For a positive integer \(M\) the paper investigates the sequences \(x_1, x_2, x_3,\dots\) of nonnegative integers, where \(0\leq x_i< M\) and \(x_{n+1}\equiv x_n^2\pmod M\) for \(n\geq 1\). These sequences are obviously periodic for any initial term \(x_1\). The author shows many properties of the sequences using the elementary properties of congruences. Graph representations of the results are also presented.

Reviewer: P.Kiss (Eger)

MSC:

11B50	Sequences (mod \(m\))
11A07	Congruences; primitive roots; residue systems
05C25	Graphs and abstract algebra (groups, rings, fields, etc.)

Keywords:

iteration; residue classes; cycles; periodic sequences; congruences