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

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)


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