On the period mod $m$ of polynomially-recursive sequences: a case study
Number Theory
2019-03-07 v2 Combinatorics
Abstract
Polynomially-recursive sequences generally have a periodic behavior mod . In this paper, we analyze the period mod of a second order polynomially-recursive sequence. The problem originally comes from an enumeration of avoiding pattern permutations and appears to be linked with nice number theory notions (the Carmichael function, Wieferich primes, algebraic integers). We give the mod supercongruences, and generalize these results to a class of recurrences.
Cite
@article{arxiv.1903.01986,
title = {On the period mod $m$ of polynomially-recursive sequences: a case study},
author = {Cyril Banderier and Florian Luca},
journal= {arXiv preprint arXiv:1903.01986},
year = {2019}
}