Divisibility Properties of Recurrent Sequences - Plankis, T. (Nonlinear Analysis: Modelling and Control, 2008)
Let m, r ∈ N. We will show, that the recurrent sequences xn = xnrn−1 + 1 (mod g), xn = xn!n−1 + 1 (mod g) and xn = xrnn−1 + 1 (mod g) are periodic modulo m, where m ∈ N, and we will find some estimations of periods and pre-periodic parts. Later we will give an algorithm sophisticated enough for finding periods length in polynomial time.