The Period and Rank of the Complex-type Padovan-p Numbers Modulo m

Abstract

In this paper, we study the complex-type Padovan-p sequence modulo m and then we give some results concerning the periods and the ranks of these sequences for any p and m. Furthermore, we produce the cyclic groups using the multiplicative orders of the generating matrices of the complex-type Padovan-p sequences when read modulo m. Finally, we give the relationships between the periods of the complex-type Padovan-p sequences modulo m and the orders of the cyclic groups produced.