Introduction

Abstract

The study of integer solutions to Diophantine equations is a topic that is almost as old as mathematics itself. Since its inception at the hands of Diophantus of Alexandria in 250 A.D., it has been found to relate to virtually every mathematical field. Suppose that we are given a polynomial f ∈ ℤ[x1,..,xn] and write 1.1 (formula presented) for the corresponding locus of non-zero integer solutions. There are a number of basic questions that can be asked about the set Sf. When is Sf non-empty?How large is Sf when it is non-empty?When Sf is infinite can we describe the set in some way?