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On the irreducibility of the non-reciprocal part of polynomials of the form $f(x) x^n + g(x)$

Volume 196 / 2020

Michael Filaseta, Huixi Li, Frank Patane, Dane Skabelund Acta Arithmetica 196 (2020), 187-201 MSC: Primary 11R09; Secondary 12E05, 11C08, 13P05. DOI: 10.4064/aa190907-11-2 Published online: 31 August 2020


A recent paper of Sawin, Shusterman and Stoll introduces the notion of robust pairs of polynomials in $\mathbb Z[x]$ and shows that under a condition of robustness the polynomial $f(x) x^{n} + g(x)$ has an irreducible non-reciprocal part provided $n$ is larger than an explicit bound depending only on $f(x)$ and $g(x)$. We establish an improved lower bound.


  • Michael FilasetaDepartment of Mathematics
    University of South Carolina
    Columbia, SC 29208, U.S.A.
  • Huixi LiDepartment of Mathematics and Statistics
    University of Nevada – Reno
    Reno, NV 89557, U.S.A.
  • Frank PataneMathematics and Computer Science Department
    Samford University
    Birmingham, AL 35209, U.S.A.
  • Dane SkabelundDepartment of Mathematics
    Virginia Tech
    Blacksburg, VA 24061, U.S.A.

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