Date of Award

5-1-2003

Degree Type

Thesis

University or Center

Clark Atlanta University(CAU)

School

School of Arts and Sciences

Degree Name

M.S.

Department

Mathematical Sciences

First Advisor

Dr. J. Ernest Wilkins, Jr.

Second Advisor

Dr. James Ponnley

Third Advisor

Dr. F. Semwogerere

Abstract

We study the cardinal number of the class of triples of consecutive positive integers such that the first of them is the product of a prime numbers, the second the product of b prime numbers, and the third the product of c prime numbers. This set of triples is denoted as Pabc and any such triple is called a CKlamkin triple. We find that the sets Pa11, P11c, P121, P212, P213, and P312 are finite, and list all the triples in each of these sets. Every other set Pabc, is infinite. This last result depends on a special case of an unproved, but very plausible, conjecture of Bateman and Horn.

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