Representation of Integers in the Form x^2+ky^2-lz^2

Abstract

For positive integers k and l, we call l a k-special if every integer can be represented in the form x^2+ky^2-lz^2 where x, y, and z are non-zero integers. In this thesis, we find the necessary and sufficient conditions for 1-special and find the conditions for an odd positive integer l to be k-special.