Abstract
Given positive integers a and n with (a,n)=1, we consider the Fermat–Euler dynamical system \(\hat{a}\) defined by the multiplication by a acting on the set of residues modulo n relatively prime to n. Given an integer M>1, the integers n for which the number of orbits of this dynamical system is a multiple of M form an ideal in the multiplicative semigroup of odd integers. We provide new results on the arithmetical properties of these ideals by using the topological properties of some directed graphs (the monads).
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Uribe-Vargas, R. Arithmetics of the numbers of orbits of the Fermat–Euler dynamical systems. Funct. Anal. Other Math. 1, 71–83 (2006). https://doi.org/10.1007/s11853-007-0005-9
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DOI: https://doi.org/10.1007/s11853-007-0005-9