A note on repunit number sequence

Authors

DOI:

https://doi.org/10.22481/intermaths.v5i1.14922

Keywords:

Horadan-type sequence, Perfect power, Repunit sequence, Tagiuri-Vajda Identity

Abstract

In this paper, we investigate the classical identities of the repunit sequence with integer indices in light of the properties of Horadan-type sequences. We highlight particularly the Tagiuri-Vajda Identity and Gelin-Cesàro Identity. Additionally, we prove that no repunit is a perfect power, either even or odd. Finally, we address a divisibility criterion for the terms of repunit  rn by a prime p and its powers.

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References

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Published

2024-06-30

How to Cite

Santos, D. C., & Costa, E. A. (2024). A note on repunit number sequence. INTERMATHS, 5(1), 54-66. https://doi.org/10.22481/intermaths.v5i1.14922

Issue

Vol. 5 No. 1 (2024)

Section

Artigos

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