A Matrix Approach for Generalizing Two Curious Divisibility Properties

Abstract

We shall consider two curious divisibility properties due to [1, 5]. Our main purpose is to generalize these properties for a general second order linear recursion. We use generating matrix approach for our purposes. By using our results, we derive a new recursive identities for two general second order linear recurrences. We give a more general result extending earlier divisibility properties on the similar subject.