On the properties of fibotomic polynomials
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866915353694568448 |
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| author | Byer, Cameron Dvorachek, Tyler Eckard, Emily Harrington, Joshua Wise, Lindsey Wong, Tony W. H. |
| author_facet | Byer, Cameron Dvorachek, Tyler Eckard, Emily Harrington, Joshua Wise, Lindsey Wong, Tony W. H. |
| contents | Define the $n$-th fibotomic polynomial to be the product of the monic irredicible factors of the $n$-th Fibonacci polynomial which are not factors of any Fibonacci polynomial of smaller degree. In this paper, we prove a number of properties of the fibotomic polynomials. This includes determining the discriminant of the fibotomic polynomials and the resultant of pairs of fibotomic polynomials. Furthermore, we completely determine the factorization form of the fibotomic polynomials in prime fields. Results are also generalized for the bivariate homogenous fibotomic polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_03345 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the properties of fibotomic polynomials Byer, Cameron Dvorachek, Tyler Eckard, Emily Harrington, Joshua Wise, Lindsey Wong, Tony W. H. Number Theory 11B39, 12E10 Define the $n$-th fibotomic polynomial to be the product of the monic irredicible factors of the $n$-th Fibonacci polynomial which are not factors of any Fibonacci polynomial of smaller degree. In this paper, we prove a number of properties of the fibotomic polynomials. This includes determining the discriminant of the fibotomic polynomials and the resultant of pairs of fibotomic polynomials. Furthermore, we completely determine the factorization form of the fibotomic polynomials in prime fields. Results are also generalized for the bivariate homogenous fibotomic polynomials. |
| title | On the properties of fibotomic polynomials |
| topic | Number Theory 11B39, 12E10 |
| url | https://arxiv.org/abs/2009.03345 |