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(mod4) 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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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| 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 |
| collection | DOAJ |
| 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(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. |
| format | Article |
| id | doaj-art-7a161ae18ead4bbab1e9b9a1e3bb9fb9 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| 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(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.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 |
| work_keys_str_mv | AT ramollin therabinowitschmollinwilliamstheoremrevisited AT ramollin rabinowitschmollinwilliamstheoremrevisited |