# Finiteness of a class of Rabinowitsch polynomials

Archivum Mathematicum (2004)

- Volume: 040, Issue: 3, page 259-261
- ISSN: 0044-8753

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topSchlage-Puchta, Jan-Christoph. "Finiteness of a class of Rabinowitsch polynomials." Archivum Mathematicum 040.3 (2004): 259-261. <http://eudml.org/doc/249308>.

@article{Schlage2004,

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.},

author = {Schlage-Puchta, Jan-Christoph},

journal = {Archivum Mathematicum},

keywords = {real quadratic fields; class number; Rabinowitsch polynomials; real quadratic fields; class number},

language = {eng},

number = {3},

pages = {259-261},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Finiteness of a class of Rabinowitsch polynomials},

url = {http://eudml.org/doc/249308},

volume = {040},

year = {2004},

}

TY - JOUR

AU - Schlage-Puchta, Jan-Christoph

TI - Finiteness of a class of Rabinowitsch polynomials

JO - Archivum Mathematicum

PY - 2004

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 040

IS - 3

SP - 259

EP - 261

AB - 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.

LA - eng

KW - real quadratic fields; class number; Rabinowitsch polynomials; real quadratic fields; class number

UR - http://eudml.org/doc/249308

ER -

## References

top- Byeon D., Stark H. M., 10.1006/jnth.2001.2729, J. Number Theory 94 (2002), 177–180. Zbl1033.11010MR1904967DOI10.1006/jnth.2001.2729
- Byeon D., Stark H. M., 10.1016/S0022-314X(02)00063-X, J. Number Theory 99 (2003), 219–221. Zbl1033.11010MR1957253DOI10.1016/S0022-314X(02)00063-X
- Heath-Brown D. R., Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression, Proc. London Math. Soc. (3) 64 (1992), 265–338. (1992) Zbl0739.11033MR1143227
- Rabinowitsch G., Eindeutigkeit der Zerlegung in Primzahlfaktoren in quadratischen Zahlkörpern, J. Reine Angew. Mathematik 142 (1913), 153–164. (1913)

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