On irreducible factors of polynomials over integers
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911334928482304 |
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| author | Garg, Rishu Singh, Jitender |
| author_facet | Garg, Rishu Singh, Jitender |
| contents | In this paper, we obtain several new factorization results for certain classes of polynomials having integer coefficients. In doing so, we use the information about prime factorization of the value taken up by such polynomials and their higher order formal derivatives at sufficiently large integer arguments. If a lower bound for the minimum possible degree of a factor of such a polynomial is known a priori, then the integer argument becomes significantly smaller, which makes the underlying factorization result easier to apply. A result on explicit lower degree factor bound for the classes of polynomials considered in this paper is also proved via Newton polygons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On irreducible factors of polynomials over integers Garg, Rishu Singh, Jitender Number Theory Commutative Algebra Algebraic Geometry 12E05, 11C08 In this paper, we obtain several new factorization results for certain classes of polynomials having integer coefficients. In doing so, we use the information about prime factorization of the value taken up by such polynomials and their higher order formal derivatives at sufficiently large integer arguments. If a lower bound for the minimum possible degree of a factor of such a polynomial is known a priori, then the integer argument becomes significantly smaller, which makes the underlying factorization result easier to apply. A result on explicit lower degree factor bound for the classes of polynomials considered in this paper is also proved via Newton polygons. |
| title | On irreducible factors of polynomials over integers |
| topic | Number Theory Commutative Algebra Algebraic Geometry 12E05, 11C08 |
| url | https://arxiv.org/abs/2512.20262 |