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September 24, 20250 citationsOpen Access

On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms

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MFMichael FilasetaAKAlexandros Kalogirou

Key Points

  • The polynomial F(x) shows irreducibility for almost all positive integer choices of n1, …, nk.
  • Consideration of cyclotomic factors leads to insights about the structure of polynomials.
  • The results build on previous findings from Schinzel, expanding the understanding of polynomial behavior.
  • The investigation focuses on specific cases of 0,1-polynomials that are important in number theory.

Abstract

We provide an alternative exposition of a result due to Schinzel. Fix an integer k 2. For almost all choices of positive integers n₁ < < n₊, we show that the polynomial F (x) = 1 + x^n₁ + + x^n₊, removed of its cyclotomic factors, is irreducible.

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Cite This Study

Filaseta et al. (2025) studied this question.

synapsesocial.com/papers/68d6e1978b2b6861e4c404a1https://doi.org/10.48550/arxiv.2508.12242
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