A A note about the repunit matrix - Santos, Douglas Catulio; Costa, Eudes Antonio; Monteiro, Francival Santos; Souza, Vitor Manoel Alves de (C.Q.D. - Revista Eletrônica Paulista de Matemática, 2024)
The study investigates repunit sequence, characterized by a second-order linear recurrence. Employing Horadam’s sequence theory and matrix algebra, we elucidate the sequence, highlighting the central role of the generating matrix in sequence analysis. The results reveal a profound interrelationship between sequence and matrix properties. The investigation culminates in a meticulous examination of the arithmetic properties and the interpretation of the repunit matrix. Methodologically, it integrates theoretical and matrix analyses, rooted in recurrences and linear algebra, offering a comprehensive academic overview of the complexities of the sequence.