Polynomials with integer roots

2019/11/01 by Patrick Letendre, Letendre, Patrick
Mathematics · #26C10 #30C10 #30C15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.00480

openalex publication_date 2019/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F_n be the set of unitary polynomials of degree n ≥ 2 that have their roots in ℤ^*. We note Q(x) := xⁿ+a₁x^n-1+…+a_n. We show that any two fixed consecutive coefficients (a_j,a_j+1) (j ∈ \1,…,n-1\) define finitely many polynomials of F_n.

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