## 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)

### 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