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The Order of an Integer
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
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Funding: none
Opened online: 2 June 2010
Accepted by: none
Citation: Wu Genqiang,Li Yanchao,Qi Yu.The Order of an Integer[OL]. [ 2 June 2010] http://en.paper.edu.cn/en_releasepaper/content/4374329
 
 
In this article, we studied the order of an integer q modulo integer m. We discussed the order of q modulo m by the prime-power factorization of m. We first discussed this problem when m is a prower of 2; Then we discussed this problem when m is a power of an odd prime p. Finally we gave explicit results of the order of q modulo m when m is any positive integer. Moreover we gave a algorithm and C-program of the order of q modulo odd prime p. Since the factorization of the mth cyclotomic polynomial over Fq has direct relation with the order of q modulo m, then our results can be used to establish the factorization theorem of cyclotomic polynomials.
Keywords:number theory; order of an integer;cyclotomic polynomial;
 
 
 

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