Period lengths modulo n and average of terms of second order linear recurrences

0585514 - MÚ 2025 RIV DE eng J - Článek v odborném periodiku
Křížek, Michal - Somer, L.
Period lengths modulo n and average of terms of second order linear recurrences.
Integers. Electronic Journal of Combinatorial Number Theory. Roč. 24, April (2024), č. článku A36. ISSN 1553-1732
Institucionální podpora: RVO:67985840
Klíčová slova: second-order linear recurrence * Fibonacci sequence
Obor OECD: Pure mathematics
Způsob publikování: Open access
https://doi.org/10.5281/zenodo.10944025

We present results concerning when the average of the rst n terms of any sequence satisfying a certain second-order linear recurrence is an integer. These results sub-stantially generalize results of Fatehizadeh and Yaqubi concerning the Fibonacci sequence. For particular second-order linear recurrences we also explicitly determine all positive integers n for which the period of this second-order linear recurrence modulo n divides n.
Trvalý link: https://hdl.handle.net/11104/0353198