A note on periodic linear recurrence relations
Abstract
We provide an elementary proof of the fact that a sequence defined by a linear recurrence relation with integer coefficients is periodic if and only if all characteristic roots are distinct roots of unity. Additionally, we discuss the case in which the coefficients of the recurrence relation are restricted to the set {–1,0,1}.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Combinatorial Mathematics
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Notes on Number Theory and Discrete Mathematics
- Volume
- 32
- Issue
- 1
- Pages
- 1–4
- Publication date
- 12 February 2026
- Language
- EN