Home > Papers

 
 
Factorization of the Cyclotomic Polynomials Q2^(n+1)(x)
Wu Genqiang 1 #,LI Yanchao 2,Qi Yu 3
1.School of Information Engineering,Lanzhou University of Finance and Economics
2.Student Office,Lanzhou University of Finance and Economics
3.School of Information Science & Engineering,Lanzhou University
*Correspondence author
#Submitted by
Subject:
Funding: none
Opened online:17 May 2010
Accepted by: none
Citation: Wu Genqiang,LI Yanchao,Qi Yu.Factorization of the Cyclotomic Polynomials Q2^(n+1)(x)[OL]. [17 May 2010] http://en.paper.edu.cn/en_releasepaper/content/358200
 
 
In this paper we study the factorization of the polynomials 1+x^(2^n)over a field K, which have the same form as the Fermat numbers . As we notice that 1+x^(2^n) is equal to the 2^(n+1)th cyclotomic polynomials Q2^(n+1)(x), this problem can be discussed by using the theorems of cyclotomic polynomial and the factorization theorem of Q2^(n+1)(x) over a finite field has been illustrated. Moreover we find that Q2^(n+1)(x) can be factored into at least two irreducible polynomials over a finite field except some special cases.
Keywords:Algebra;cyclotomic polynomial;order of an integer;Factorization theorem
 
 
 

For this paper
  • ● PDF (0B)
  • ● Revision 0 　　 　　
  • ● Print this paper
  • ● Recommend this paper to a friend
  • ● Add to my favorite list

    Saved Papers

    Please enter a name for this paper to be shown in your personalized Saved Papers list

Tags
Add yours

Related Papers

Statistics
PDF Downloaded 229
Bookmarked 0
Recommend 5
Comments Array
Submit your papers