A question about Aurifeuillian factorizations  

作　　者：孙琦 袁平之 韩清 

机构地区：[1]Department of Mathematics, Sichuan University, Chengdu 610064, China

出　　处：《Chinese Science Bulletin》1995年第20期1681-1683,共3页

基　　金：Project supported by the National Natural Science Foundation of China.

摘　　要：Let b】1 be an integer. Aurifeuille et al. discovered a special factorization for a class of numbers in the form of bⁿ±1. It is called Aurifeuillian factorization. Let p be an odd prime. Let ζ=ζ_p denote the primitive pth root of unity exp （2πi/p）.Let （/） denote the Jacobi symbol. When p≡1 （mod 4） and N=（P^p-1）/（p-1）=P^p-1+p^P-2+…+p+1, Hahn gave the congruence equation X²≡p （mod N） the four<正> Let b>1 be an integer. Aurifeuille et al. discovered a special factorization for a class of numbers in the form of bn±1. It is called Aurifeuillian factorization. Let p be an odd prime. Let ζ=ζpdenote the primitive pth root of unity exp （2πi/p）.Let （/） denote the Jacobi symbol. When p≡1 （mod 4） and N=（Pp-1）/（p-1）=Pp-1+pP-2+…+p+1, Hahn gave the congruence equation X2≡p （mod N） the four solutions

关 键 词：Aurifeuillian FACTORIZATION cyclotomic field of PTH ROOTS of unity GALOIS group. 

分 类 号：O156[理学—数学]