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
DOI:
https://doi.org/10.1090/S0025-5718-97-00801-6
MathSciNet review:
1377660
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Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
339279
Email:
hajdul@math.klte.hu
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
