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Polynomial
irreducibility via shifts
Emi Lycan and Vadim Ponomarenko |
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Vol. 18 (2025), No. 5, 855–860
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Abstract |
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When factoring integer polynomials, it often helps to be able to tell if a polynomial is irreducible before trying (and failing) to find its factors. We examine one such irreducibility test presented by A. Bevelacqua and extend its applicability via shifts, or translations, of the polynomial. On the way there, we also encounter fixed divisors, Bunyakovsky’s conjecture, and a bound on the size of the complex roots of the polynomial. |
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Keywords
polynomial, integer polynomial, irreducibility
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Mathematical Subject Classification
Primary: 11C08
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Milestones
Received: 12 January 2024
Revised: 11 May 2024
Accepted: 3 July 2024
Published: 20 November 2025
Communicated by Scott T. Chapman
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Authors |
| Emi Lycan | |
| Hemet, CA United States |
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| Vadim Ponomarenko | |
| Department of Mathematics and
Statistics San Diego State University San Diego, CA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
