The Use of a Second-order Recurrence Relation in the Diagnosis of Breast Cancer

The purpose of this paper is to outline an application of number theory in medicine. More specifically, a linear second-order recurrence relation is utilized in a technique for the diagnosis of breast cancer. This continues a tradition in this journal of applications of second-order recurrences. Indeed, the very first issue contained an article by Basin [1] on the Fibonacci sequence in art and nature, and the tradition has been maintained over the years by such authors as Botten [2] who applied the more general sequence of Horadam to a problem in optics. Number theorists, while rightly valuing their work for its beauty and intrinsic worth, are not always aware of the extensive application of the elegant techniques they develop. In this paper we develop an inhomogeneous linear second-order recurrence relation of the form St #!#,_! B2St_2 =B3 (1.1)