Journal of Guangxi Normal University(Natural Science Edition) ›› 2011, Vol. 29 ›› Issue (3): 18-22.

Previous Articles     Next Articles

Exponent of Odd Prime Factor in Standard Factorization ofFibonacci Number

YOU Li-hua, HUANG Rong-hui   

  1. School of Mathematical Sciences,South China Normal University,Guangzhou Guangdong 510631,China
  • Received:2011-04-08 Online:2011-08-20 Published:2018-12-03

Abstract: The relationship between the exponent of odd prime factor p in the standard factorization of Fibonacci numberFn and its subscript n is presented in this paper.It shows that the exponent of odd prime factor p in the standard factorization of Fibonacci number Fn can be determined by the exponent of d(p) and p in the factorization of the subscript n,where d(p)=min{w:p|Fw}.The relationshipbetween d(p) and p is given in this paper,and an open problem on the exponent of oddprime factor p in the standard factorization of Fibonacci number Fd(p) is also proposed.

Key words: Fibonacci number, standard factorization, odd primefactor, exponent, congruence

CLC Number: 

  • O156.2
[1] 孙淑玲,许胤龙.组合数学引论[M].合肥:中国科学技术大学出版社,2004:153-157.
[2] 曹汝成.组合数学[M].广州:华南理工大学出版社,2002:91-98.
[3] 陈景润.组合数学简介[M].天津:天津科学技术出版社,1988:94-109.
[4] 昊振奎.斐波那契数列[M].沈阳:辽宁教育出版社,1987:43-152.
[5] 陈景润.组合数学[M].郑州:河南教育出版社,1985:7-10.
[6] 吴佃华.关于
Fn的一些注记[J].广西师范大学学报:自然科学版,1992,10(2):37-39.
[7] 袁明豪.Fibonacci数的一组整除特征[J].数学通讯,2004(15):29-31.
[8] 袁明豪.正Fibonacci数的标准分解式中的因子2的指数[J].数学通讯,2003(15):26-27.
[9] 袁明豪.正Fibonacci数的标准分解式中的因子3的指数[J].荆州师范学院学报:自然科学版,2003,26(2):12-13.
[10] 袁明豪.正Fibonacci数的标准分解式中的因子5的指数[J].数学的实践与认识,2007,37(7):166-170.
[11] 王念良,张洁.Fibonacci数的标准分解式中素因子7的指数[J].商洛学院学报,2007,21(4):4-7.
[12] 林丽荣,尤利华.Fibonacci数的标准分解式中素因数11的指数[J].甘肃联合大学学报:自然科学版,2008,22(6):4-10.
[13] 吴佃华,贾小英.Fibonacci数的整除性[J].广西师范学院学报:自然科学版,2007,24(3):28-30.
[14] 王志兰.费马小定理的几种证法及应用[J].廊坊师范学院学报:自然科学版,2009,9(6):11-13.
[15] 揭方琢.斐波那契数列[J].华中师范大学学报:自然科学版:数学史专辑,1987(3):72-85.
[1] WANG Junfeng, LI Ping. Shortest-path Exponent and Backbone Exponentof Explosive Percolation Model [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(2): 81-86.
[2] LEI Qingzhu,QIN Yongsong,LUO Min. Empirical Bayes Estimation and Test for Scale ExponentialFamilies under Strong Mixing Samples [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(3): 63-74.
[3] YANG Kun, LIN Jiao, JIANG Gui-rong. Dynamics Analysis of a Stochastic SIS Epidemic Model with Birth Pulses [J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(4): 81-86.
[4] XU Lun-hui, YOU Huang-yang. Short-term Traffic Flow Forecasting Based on Analysis of Characteristics and Impact Factors [J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(1): 1-5.
[5] XUE Jin-dong, FENG Chun-hua. Positive Almost Periodic Solutions for a Class of Integro-differential Equation with Impulses and Infinite Delays [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(4): 48-53.
[6] ZHANG Hao-qi, ZHANG Hao-min. Exponential Stability of 1.5 Order Stochastic Taylor Method for Stochastic Differential Equations [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(2): 35-41.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!