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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computational experiences on the distances of polynomials to irreducible polynomials


Authors: A. Bérczes and L. Hajdu
Journal: Math. Comp. 66 (1997), 391-398
MSC (1991): Primary 11C08, 11R09; Secondary 11T06, 11Y99
MathSciNet review: 1377660
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Abstract: In this paper we deal with a problem of Turán concerning the `distance' of polynomials to irreducible polynomials. Using computational methods we prove that for any monic polynomial $P\in $ ${\mathbb {Z}}[x]$ of degree $\leq 22$ there exists a monic polynomial $Q\in {\mathbb {Z}}[x]$ with deg($Q$) = deg($P$) such that $Q$ is irreducible over $\mathbb {Q}$ and the `distance' of $P$ and $Q$ is $\leq 4$.


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Additional Information

A. Bérczes
Affiliation: Department of Mathematics and Informatics, Kossuth Lajos University, 4010 Debrecen, Pf. 12, Hungary
Email: berczes@dragon.klte.hu

L. Hajdu
Affiliation: Department of Mathematics and Informatics, Kossuth Lajos University, 4010 Debrecen, Pf. 12, Hungary
Email: hajdul@math.klte.hu

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00801-6
PII: S 0025-5718(97)00801-6
Received by editor(s): July 19, 1995
Received by editor(s) in revised form: February 2, 1996
Additional Notes: Research of the second author was supported in part by Grants 014245 and T 016 975 from the Hungarian National Foundation for Scientific Research, by the Universitas Foundation of Kereskedelmi Bank RT and by Foundation for Hungarian Higher Education and Research.
Article copyright: © Copyright 1997 American Mathematical Society