THE INTEGER-VALUED POLYNOMIALS ON LUCAS NUMBERS

Abstract

An integer-valued polynomial on a subset, S, of the set of integers, Z, is a polynomial f(x) 2 Q[x] such that f(S) Z. The collection, Int(S;Z), of such integer-valued polynomials forms a ring with many interesting properties. The concept of p-ordering and the associated p-sequence due to Bhargava [2] is used for nding integer-valued polynomials on any subset, S, of Z. In this thesis, we concentrate on extending the work of Keith Johnson and Kira Scheibelhut [14] for the case S = L, the Lucas numbers, where they work on integervalued polynomials on S = F, Fibonacci numbers. We also study integer-valued polynomials on the general 3 term recursion sequence, G, of integers for a given pair of initial values with some interesting properties. The results are well-agreed with those of [14].