Modified Cyclotomic Polynomial and Its Irreducibility

Ki-Suk Lee, Sung-Mo Yang and Soon-Mo Jung
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Ki-Suk Lee: Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
Sung-Mo Yang: Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
Soon-Mo Jung: College of Science and Technology, Hongik University, Sejong 30016, Korea

Mathematics, 2020, vol. 8, issue 3, 1-12

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.

Keywords: irreducible polynomial; cyclotomic polynomial; modified cyclotomic polynomial; semi-cyclotomic polynomial; multiplicative group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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