International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 819068, 14 pages
Research Article

The Rabinowitsch-Mollin-Williams Theorem Revisited

Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4, Canada

Received 24 April 2009; Revised 24 June 2009; Accepted 20 August 2009

Academic Editor: Aloys Krieg

Copyright © 2009 R. A. Mollin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We completely classify all polynomials of type (x2+x(Δ1))/4 which are prime or 1 for a range of consecutive integers x0, called Rabinowitsch polynomials, where Δ1(mod4) with Δ>1 square-free. This corrects, extends, and completes the results by Byeon and Stark (2002, 2003) via the use of an updated version of what Andrew Granville has dubbed the Rabinowitsch-Mollin-Williams Theorem—by Granville and Mollin (2000) and Mollin (1996). Furthermore, we verify conjectures of this author and pose more based on the new data.