Lower bounds for periods of Ducci sequences
Florian Breuer, Igor E. Shparlinski · NOVA (University of Newcastle Australia) · 2020
A Ducci sequence is a sequence of integer n-tuples obtained by iterating the map: D:(a1,a2,…,an)↦(|a1−a2|,|a2−a3|,…,|an−a1|). Such a sequence is eventually periodic and we denote by P(n) the maximal period of such sequences for given odd n. We prove a lower bound for P(n) by counting certain partitions. We then estimate the size of these partitions via the multiplicative order of two modulo n.