Empirical estimates of the average orders of orbits period lengths in Euler groups

Abstract

The averaged growth rate of period's length of the geometrical progressions {q t modn, t=0,1,…} for increasing n is empirically estimated for different values of q. The experimental results, obtained for n up to 10 6, allow us to conjecture that the average order of period's length is C n ln(n) , where constant C depends on q. To cite this article: F. Aicardi, C. R. Acad. Sci. Paris, Ser. I 339 (2004).