The Rabinowitsch-Mollin-Williams Theorem Revisited

We completely classify all polynomials of type (x2+x−(Δ−1))/4 which are prime or 1 for a range of consecutive integers x≥0, called Rabinowitsch polynomials, where Δ≡1(mod⁡4) with Δ>1 square-free. This corrects, extends, and completes the results by Byeon and Stark (2002, 2003) via the use of an...

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Main Author: R. A. Mollin
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2009/819068
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author R. A. Mollin
author_facet R. A. Mollin
author_sort R. A. Mollin
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description We completely classify all polynomials of type (x2+x−(Δ−1))/4 which are prime or 1 for a range of consecutive integers x≥0, called Rabinowitsch polynomials, where Δ≡1(mod⁡4) 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.
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spelling doaj-art-7a161ae18ead4bbab1e9b9a1e3bb9fb92025-08-20T02:07:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/819068819068The Rabinowitsch-Mollin-Williams Theorem RevisitedR. A. Mollin0Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4, CanadaWe completely classify all polynomials of type (x2+x−(Δ−1))/4 which are prime or 1 for a range of consecutive integers x≥0, called Rabinowitsch polynomials, where Δ≡1(mod⁡4) 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.http://dx.doi.org/10.1155/2009/819068
spellingShingle R. A. Mollin
The Rabinowitsch-Mollin-Williams Theorem Revisited
International Journal of Mathematics and Mathematical Sciences
title The Rabinowitsch-Mollin-Williams Theorem Revisited
title_full The Rabinowitsch-Mollin-Williams Theorem Revisited
title_fullStr The Rabinowitsch-Mollin-Williams Theorem Revisited
title_full_unstemmed The Rabinowitsch-Mollin-Williams Theorem Revisited
title_short The Rabinowitsch-Mollin-Williams Theorem Revisited
title_sort rabinowitsch mollin williams theorem revisited
url http://dx.doi.org/10.1155/2009/819068
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