On integer sequences in product sets

Abstract

Let B be a finite set of natural numbers or complex numbers. Product set corresponding to B is defined by B.B:={ab:a,b∈B}. In this paper we give an upper bound for longest length of consecutive terms of a polynomial sequence present in a product set accurate up to a positive constant. We give a sharp bound on the maximum number of Fibonacci numbers present in a product set when B is a set of natural numbers and a bound which is accurate up to a positive constant when B is a set of complex numbers.