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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.

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