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Modified Cyclotomic Polynomial and Its Irreducibility

Author

Listed:
  • Ki-Suk Lee

    (Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
    These authors contributed equally to this work.)

  • Sung-Mo Yang

    (Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
    These authors contributed equally to this work.)

  • Soon-Mo Jung

    (College of Science and Technology, Hongik University, Sejong 30016, Korea
    These authors contributed equally to this work.)

Abstract

Finding irreducible polynomials over Q (or over Z ) is not always easy. However, it is well-known that the m th cyclotomic polynomials are irreducible over Q . In this paper, we define the m th modified cyclotomic polynomials and we get more irreducible polynomials over Q systematically by using the modified cyclotomic polynomials. Since not all modified cyclotomic polynomials are irreducible, a criterion to decide the irreducibility of those polynomials is studied. Also, we count the number of irreducible m th modified cyclotomic polynomials when m = p α with p a prime number and α a positive integer.

Suggested Citation

  • Ki-Suk Lee & Sung-Mo Yang & Soon-Mo Jung, 2020. "Modified Cyclotomic Polynomial and Its Irreducibility," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:343-:d:328126
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