Finiteness of a class of Rabinowitsch polynomials

Jan-Christoph Schlage-Puchta

 Mathematisches Institut, Eckerstr. 1, 79111 Freiburg, Germany


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.