A note on repunit number sequence

Douglas Catulio Santos; Eudes Antonio Costa

doi:10.22481/intermaths.v5i1.14922

Authors

Douglas Catulio Santos https://orcid.org/0000-0002-5221-6087
Eudes Antonio Costa https://orcid.org/0000-0001-6684-9961

DOI:

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

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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