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Reciprocal Monogenic Septinomials of Degree 2n3

Lenny Jones

Lenny Jones

Professor Emeritus, Department of Mathematics, Shippensburg UniversityShippensburg, USA
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Jones, Lenny
  
Feb 21, 2024
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Published Online: Feb 21, 2024
Page range: 155 - 169
Received: Jun 11, 2023
Accepted: Jan 24, 2024
DOI: https://doi.org/10.2478/amsil-2024-0003
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© 2024 Lenny Jones, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Examples for (3_8) and their factorizations

(Â, B̂) (A, B) Factorization of ℱn,A,B(x)
(0, 0) (4, 24) (x2n+1 + 36x2n−1 3 + 434x2n + 36x2n−1 + 1)Φ2n+1 (x)
(0, 1) (4, 357) (x2n + 3x2n−1 + 1)(x2n+1 + 33x2n−1 3 + 335x2n + 33x2n−1 + 1)
(0, 3) (4, 591) (x2n + 9x2n−1 + 1)(x2n+1 + 27x2n−13 + 191x2n + 27x2n−1 + 1)
(1, 0) (1, 24) (x2n + 6x2n−1 + 1)(x2n+1 + 3x2n−13 + 11x2n + 3x2n−1 + 1)
(1, 2) (1, 6) (x2n+1 + 9x2n−13 + 29x2n + 92n−1 + 1)Φ2n+1 (x)
(1, 3) (1, 15) (x2n + 3x2n−1 + 1)3
(2, 0) (2, 12) (x2n+1 + 18x2n−13 + 110x2n + 18x2n−1 + 1)Φ2n+1 (x)
(2, 1) (2, 93) (x2n + 9x2n−1 + 1)(x2n+1 + 9x2n−13 + 29x2n + 9x2n−1 + 1)
(2, 3) (2, 75) (x2n + 3x2n−1 + 1)(x2n+1 + 15x2n−13 + 65x2n + 15x2n−1 + 1)
(3, 0) (3, 252) (x2n + 6x2n−1 + 1)(x2n+1 + 21x2n−1 3 + 119x2n + 21x2n−1 + 1)
(3, 1) (3, 189) (x2n + 3x2n−1 + 1)(x2n+1 + 24x2n−1 3 + 173x2n + 24x2n−1 + 1)
(3, 2) (3, 18) (x2n+1 + 27x2n−1 3 + 245x2n + 27x2n−1 + 1)Φ2n+1 (x)
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Mathematics, General Mathematics
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