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The Rabinowitsch-Mollin-Williams theorem revisited. (English) Zbl 1290.11151
Summary: We completely classify all polynomials of type $$(x^2+x - (\Delta - 1))/4$$ which are prime or 1 for a range of consecutive integers $$x\geq 0$$, called Rabinowitsch polynomials, where $$\Delta \equiv 1\pmod 4$$ with $$\Delta >1$$ square-free. This corrects, extends, and completes the results by Byeon and Stark via the use of an updated version of what Andrew Granville has dubbed the Rabinowitsch-Mollin-Williams Theorem by A. Granville and the author [Acta Arith. 96, No. 2, 139–153 (2000; Zbl 0985.11040) and the author[Quadratics. Boca Raton, FL: CRC Press (1996; Zbl 0858.11001). Furthermore, we verify conjectures of this author and pose more based on the new data.

##### MSC:
 11R29 Class numbers, class groups, discriminants 11R09 Polynomials (irreducibility, etc.)
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