Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
real quadratic fields; class number; Rabinowitsch polynomials
real quadratic fields; class number; Rabinowitsch polynomials
Summary:
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.
References:
[1] Byeon D., Stark H. M.: On the Finiteness of Certain Rabinowitsch Polynomials. J. Number Theory 94 (2002), 177–180. DOI 10.1006/jnth.2001.2729 | MR 1904967 | Zbl 1033.11010
[2] Byeon D., Stark H. M.: On the Finiteness of Certain Rabinowitsch Polynomials. II. J. Number Theory 99 (2003), 219–221. DOI 10.1016/S0022-314X(02)00063-X | MR 1957253 | Zbl 1033.11010
[3] 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. MR 1143227 | Zbl 0739.11033
[4] Rabinowitsch G.: Eindeutigkeit der Zerlegung in Primzahlfaktoren in quadratischen Zahlkörpern. J. Reine Angew. Mathematik 142 (1913), 153–164.
Search
Partner of
