A NOTE ON REPUNIT NUMBER SEQUENCE

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.

Keywords

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