Periods and Young's diagram of Fermat-Euler's geometrical progressions of residues
The paper under review is an excellent paper that is full of ideas for interested researchers in the subject. Let \(n\) be a positive integer and consider the geometric sequence of residues modulo \(n\); \[ \{a^{t}\mid t=1,2,\dots\}\pmod n \] for \(a \in {\mathbb Z}_n\). Such sequence is always periodic starting from some place, \[ a^{t+T(a,n)}\equiv a^t\pmod n \] for every sufficiently large \(t\). What is the minimal period length \(T(a,n)\) of this sequence? The corresponding Young diagram of \(n\) values of \(T(a,n)\), describes the partition of \(n\) residues \(a\) into the classes, for whose sequence the period's length has a fixed value. The author of the paper under review studies the arithmetic and statistical properties of the function \(T(a,n)\) of natural variables \(a\) and \(n\). The author's clever presentation and approach to the problem guides readers to a world of interested questions for further investigations and research.
scientific article; zbMATH DE number 5826919