Finiteness of a class of Rabinowitsch polynomials. (English) Zbl 1122.11070

The author shows that there are only finitely many Rabinowitsch polynomials, i.e., there are only finitely many positive integers \(m\) such that there is some integer \(t\) such that \(| n^2+n-m| \) is 1 or a prime for all \(n\in [t+1, t+\sqrt {m}]\). As the author points out in his note added in proof, this result has been also obtained by D. Byeon and H. M. Stark [ J. Number Theory 99, No. 1, 219–221 (2003; Zbl 1033.11010)] and by S. Louboutin.


11R11 Quadratic extensions
11R29 Class numbers, class groups, discriminants
11C08 Polynomials in number theory


Zbl 1033.11010
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