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On the Finiteness of Certain Rabinowitsch Polynomials

✍ Scribed by Dongho Byeon; H.M. Stark

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
67 KB
Volume
94
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let m be a positive integer and f m (x) be a polynomial of the form f m (x)=x 2 +x -m. We call a polynomial f m (x) a Rabinowitsch polynomial if for t=[ `m] and consecutive integers x=x 0 , x 0 +1, ..., x 0 +t -1, |f(x)| is either 1 or prime. In this note, we show that there are only finitely many Rabinowitsch polynomials f m (x) such that 1+4m is square free.

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