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《Journal of Zhejiang University(Science Edition)》 2010-03
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Some new solutions of the congruence 2~(n-2)≡1(mod n)

YANG Shi-chun(1.Department of Mathematics,Aba Teacher's College,Wenchuan 623000,Sichuan Province,China;2.College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China)  
In 1991,all solutions of the congruence 2n-2≡1(mod n) up to 1011have been presented by Sinisalo M.K,and all 88 solutions in the interval [3,1011] have been tabulated and,only 6 final decimal digit 9 have been obtained.It is proved that there does not exist any solution n3.462*1014 for congruence 2n-2≡1(mod n) having square divisors.By using a new method,it has been found that there exist 9 solutions for congruence 2n-2≡1(mod n) having square divisors.By using the same method,the new solutions n of the congruence 2n-2≡1(mod n),where n1011 have been tabulated.
【Key Words】: congruence solutions square divisors
【Fund】: 四川省科技厅应用基础研究项目(2009JY0091);; 阿坝师专校级科研课题资助(ASA-0913)
【CateGory Index】: O156.1
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【Citations】
Chinese Journal Full-text Database 4 Hits
1 YANG Shi-chun (Aba Teachers College, Dujiangyan 611830, China);On solutions to the diuphantion equation f(x)=(y~n-1)/(y-1)[J];Journal of Zhejiang University(Sciences Edition);2005-02
2 Zhang Mingzhi (Department of mathematics);A NOTE ON THE CONGRUENCE 2~(n-2)=1(mod n)[J];Journal of Sichuan University (Natural Science Edition);1990-02
3 LIU Xian-bei (Department of Mathematics,Anhui Normal University,Anhui Wuhu 241000,China);Remarks on the Solutions to the Congruence 2~(n-2)≡1(mod n)[J];Journal of Sichuan University (Natural Science Edition);2005-06
4 YANG Shi-chun ( Department of Mathematics,Aba Teacter’s College,Wenchuan 623000,P. R. C. );The note to the solutions of the congruence 2~(n-2)≡1(mod n)[J];Journal of Southwest University for Nationalities(Natural Science Edition);2007-06
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 YANG Shi-chun (Aba Teachers College,Wenchuan,Sichuan,623000,China);Some Results Concerning Odd Perfect Numbers of the Form N = π~α 3~(2β)Q~(2β)[J];Journal of ABA Teachers College;2006-04
2 YANG Shi-chun,WU Wen-quan (Math Dept.of Aba Teachers College,Wenchuan Sichuan 623000,China);Probes into "Low Starting Point and High Qualities" Curriculum Building Mode of Elementary Number Theory[J];Journal of ABA Teachers College;2007-03
3 Jiang Zi-guo1,Cao Xing-bing2(Math Dept.of Aba Teachers College,Wenchuan Sichuan,623000)(Chongqing 37th Middle school,Dadukou Chongqing,400084,China);On the Solution to Diophantine equation[(10k_1+2)~n-1] [(10k_2+5)~n-1]=x~2[J];Journal of ABA Teachers College;2007-03
4 WU Xin-sheng (The 16th Electronic Research Institute of the Ministry of Information Industry, Hefei 230061,China);The Representation of Large Even Integer as a Sum of Two Primes[J];Journal of Anhui Tv University;2001-01
5 WU Xin-sheng(The 16th Electronic Research Institute of the Ministry of Information Industr y,Hefei,230061,China)<IMG SRC="IMAGE/01220072.JPG" HEIGHT=30 WIDTH=49>;A Research Report about Primes with P+2 Form[J];Journal of Anhui Tv University;2002-04
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7 WU Xin-sheng(16th Electronic Research Institute,Ministry of Information Industry,Hefei 230061,China);Research of Solutians of Series for Indeterminate Equatian x_1~2+x_2~2+…+x_k~2=w[J];Journal of Anhui Radio & TV University;2008-01
8 SUN Xue-gong1,2 (1.School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China;2.Department of Mathematics and Physics Science,Huanhai Institute of Technology,Lianyungang 222005,China);On the sums of reciprocals of square-free numbers[J];Journal of Anhui University(Natural Sciences);2008-04
9 Lu Yeguang (Hefei Institute of Economics and Technology);On the U-Cyclic Rings and Double Cyclic Rings[J];JOURNAL OF ANHUI UNIVERSITY(NATURAL SCIENCES);1994-04
10 LIANG Wei-xiang(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China);Discussion on Solutions of Equation σ(n)=kn,k≥2[J];Journal of Anhui Normal University(Natural Science);2008-06
【Secondary Citations】
Chinese Journal Full-text Database 4 Hits
1 Zhang Mingzhi (Department of mathematics);A NOTE ON THE CONGRUENCE 2~(n-2)=1(mod n)[J];Journal of Sichuan University (Natural Science Edition);1990-02
2 LIU Xian-bei (Department of Mathematics,Anhui Normal University,Anhui Wuhu 241000,China);Remarks on the Solutions to the Congruence 2~(n-2)≡1(mod n)[J];Journal of Sichuan University (Natural Science Edition);2005-06
3 LE Mao Hua (Department of Mathematics, Zhanjiang Normal College, Zhanjiang 524048, P. R. China);On Goormagthtigh's Equation (x~3-1)/(x-1)=(y~n-1)/(y-1)[J];Acta Mathematica Sinica;2002-03
4 YUAN Ping-zhi; LUO Jia-gui ( Dept. of Math. & Mech., Changsha Aailway Institute, Changsha 410075, China; Dept. of Math., Sichuan University, Chengdu 610064, China);On Solutions of Higher Degree Diophantine Equation[J];Journal of Mathematical Research and Exposition;2001-01
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