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Finiteness of a class of Rabinowitsch polynomials

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*Jan-Christoph Schlage-Puchta*

**Address.**

Mathematisches Institut, Eckerstr. 1, 79111 Freiburg,
Germany

**E-mail. **jcp@arcade.mathematik.uni-freiburg.de

**Abstract.**

We prove that 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 $n\in[t+1, t+\sqrt{m}]$, thus solving a problem of Byeon and Stark.

**AMSclassification. **11R11, 11R20.

**Keywords. **Real quadratic fields, class number, Rabinowitsch
polynomials.