Computational experiences on the distances of polynomials to irreducible polynomials
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- by A. Bérczes and L. Hajdu PDF
- Math. Comp. 66 (1997), 391-398 Request permission
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 $\leq 4$.References
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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.
- © Copyright 1997 American Mathematical Society
- 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