On the period mod m of polynomially-recursive sequences: a case study

2019/03/05 by Cyril Banderier, Florian Luca, Banderier, Cyril +1
Computer Science · Mathematics · #05A15 #11B39 #11B50 #11B85 #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1903.01986

openalex publication_date 2019/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Polynomially-recursive sequences generally have a periodic behavior mod m. In this paper, we analyze the period mod m 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 a^k supercongruences, and generalize these results to a class of recurrences.

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