SOME PROPERTIES OF THE PRODUCT OF (P,Q) – FIBONACCI AND (P,Q) - LUCAS NUMBER

Abstract

Some mathematicians study the basic concept of the generalized Fibonacci sequence and Lucas sequence which are the (p,q) – Fibonacci sequence and the (p,q) – Lucas sequence. For example, Singh, Sisodiya and Ahmad studied the product of the k-Fibonacci and k-Lucas numbers. Moreover, Suvarnamani and Tatong showed some results of the (p, q) - Fibonacci number. They found some properties of the (p,q) – Fibonacci number and the (p,q) – Lucas number. There are a lot of open problem about them. Moreover, the example for the application of the Fibonacci number to the generalized function was showed by Djordjevicand Srivastava. In this paper, we consider the (p,q) – Fibonacci sequence and the (p,q) – Lucas sequence. We used the Binet’s formulas to show that some properties of the product of the (p,q) – Fibonacci number and the (p,q) – Lucas number. We get some generalized properties on the product of the (p,q) – Fibonacci number and the (p,q) – Lucas number.