On Gaussian and Quaternion Repunit Numbers - Costa, Eudes Antonio; Santos, Douglas Catulio; Catarino, Paula Maria Machado Cruz; Spreafico, Elen Viviani Pereira (Revista de Matemática da UFOP, 2024)
This work introduces two new sequences: the gaussian repunit numbers and the quaternion repunit numbers. We establish some properties of these sequences, as well as, recurrence relations, the Binet formula, and Catalan's, Cassini's, and d'Ocganes identities.