JOURNAL ARTICLE

Shifted Power of a Polynomial with Integral Roots.

  • Published In: Mathematica Slovaca, 2023, v. 73, n. 4. P. 883 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Dubickas, Artūras 3 of 3

Abstract

In this note, for any integers m, n ≥ 2, we find a condition on a positive integer c under which there exists a monic polynomial f ∈ ℤ [ x ] of degree n for which f(x)m – c has mn integral roots counting with multiplicities. This is the case if and only if m = 2 and c is a constant that comes from a solution of the Prouhet-Tarry-Escott problem of size n. For example, the smallest positive integer c for which there exists a monic degree 7 polynomial f ∈ ℤ [ x ] such that f(x)2–c has 14 integral roots is c = 6620176679276160000. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Mathematica Slovaca. 2023/08, Vol. 73, Issue 4, p883
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2023
  • ISSN:0139-9918
  • DOI:10.1515/ms-2023-0065
  • Accession Number:169788242
  • Copyright Statement:Copyright of Mathematica Slovaca is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.