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 -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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