Abstract

Let n a be positive integer. The Catalan matrix of order n, denoted by ϐ<inf>n</inf>[x], is a lower triangular Toeplitz matrix whose nonzero elements are expressions containing Catalan numbers and a real parameter x. In this paper, we investigate the multiplicative order of the cyclic group generated by ϐn[x] (for x 2 N) modulo a positive integer m.