Full-Text Search:
Home|Journal Papers|About CNKI|User Service|FAQ|Contact Us|中文
《Journal of Chongqing Teachers College(Natural Science Edition)》 2003-01
Add to Favorite Get Latest Update

On the Diophantine Equation x~3+1=7y~2

LUO Ming (College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047,China)  
In this paper the author has proved that the Diophantine equation x3+1=7y2 has only integer solutions (x,y)=(-1,0),(3,±2).
【Fund】: 重庆市教委基金项目 (96 0 3 84)资助
【CateGory Index】: O122.2
Download(CAJ format) Download(PDF format)
CAJViewer7.0 supports all the CNKI file formats; AdobeReader only supports the PDF format.
【References】
Chinese Journal Full-text Database 10 Hits
1 YU zhao-yang(Department of Engineering,Xichang College,Xichang 615013,China);On the Diophantine Equation x~3-1=13y~2[J];Journal of Chongqing Institute of Technology;2006-11
2 ZHENG Zi-xia(College of Mathematics and Computer,Chongqing Normal University,Chongqing 400047,China);On Diophantine Equation[J];Journal of Chongqing Institute of Technology(Natural Science);2008-05
3 ZHU De-hui(College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China);On the Diophantine Equation y~2-3y~4=166[J];Journal of Chongqing Normal University(Natural Science);2008-03
4 ZHENG Zi-xia(College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China);On the Diophantine Equation x~2-7y~4=93[J];Journal of Chongqing Normal University(Natural Science);2008-04
5 ZHU De-hui(College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China);On the Diophantine Equation x~2-3y~4=286[J];Journal of Chongqing Normal University(Natural Science);2008-04
6 DUAN Hui - ming, FENG Guo - feng (Department of Mathematics and Computer Science Chongqing Normal University, Chongqing 400047, China);A New Way to Prove the Indetints[J];Journal of Chongqing Vocational & Technical Institute;2004-03
7 DUAN Hui-ming(School of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China);On the diophantine equation x~3+1=35_y~2[J];Journal of Science of Teachers College and University;2005-02
8 DUAN Hui-ming(School of Computer Science and Technology,Chongqing University of Post and Telecommunications,Chongqing 400065,China);On the Diophantine equation x~3+1=86y~2[J];Journal of Science of Teachers' College and University;2007-02
9 ZHU De-hui(College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China);About the diophantine equation x~2-3y~4=97[J];Journal of Changchun University of Technology(Natural Science Edition);2008-02
10 ZHAN Jin-hu(Department of Mathematics,Northwest University,Xi'an 710069,P.R.China);On the Diophantine Equation x~3±8=Dy~2[J];Science Technology and Engineering;2009-01
【Citations】
Chinese Journal Full-text Database 2 Hits
1 Wang Zhenjiang, Tong Ruizhou(Dept. of Maths., Chaoyang normal college, Liaoning);On the Diophantus Equation x~3 + 1 = l3y~2 xy≠0[J];Journal of Natural Science of Heilongjiang University;1991-04
2 Sun Qi;ON THE DlOPHANTlNE EQUATION[J];Journal of Sichuan University (Natural Science Edition);1987-01
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 WU Wen-quan1,HE Bo2(1.Mathematics Department of Aba Teachers College,Wenchuan Sichuan,623000 China; 2.Longchang Xiangshi High School,Longchang Sichuan 642152 China);A Conjecture of the Lucas Triangle[J];Journal of ABA Teachers College;2006-03
2 LI Xiao-yan,ZHANG Hui(School of Mathematics Science,Anhui University,Hefei 230039,China);On the Diophantine Equation x~2+D=4y~3[J];Journal of Hefei Teachers College;2009-03
3 MU Shan-zhi1,DAI Xi-min2(1.Department of Foundation Course,Jiangsu Teachers College of Technology,Changzhou 213001,China;2.School of Sciences,Hefei University of Technology,Hefei 230009,China);On the diuphantine equation x~3±1=py~2[J];Journal of Anhui University(Natural Sciences);2008-01
4 SUN Guang-ren(School of Math.and Computation Science,Anqing Teachers College,Anqing 246133,China);Total Number of Solutions of a Family of Exponential Diophantine Equations with a Parameter[J];Journal of Anqing Teachers College(Natural Science Edition);2009-01
5 GUAN Xun-gui(Department of Mathematics of Taizhou Normal College,Taizhou 225300,China);On the Indeterminate Equation x~n+y~n=y~(n-2)z~2[J];Journal of Anqing Teachers College(Natural Science Edition);2009-01
6 WANG Hong-chang(Yingkou Occupation Techniuqe College,Yingkou 115000,China);On diophantine equation x~4+py~4=z~2[J];Journal of University of Science and Technology Liaoning;2009-02
7 Ji wanhui Zhang hong tu;on the Diophanline Eqhation (1/n) sum from (k=0) to (n-1)[1+(40s21)K]~r=[1+(40s+21)n]~r[J];Journal of Anshun Teachers College;1994-02
8 Ji wanhui Ning Xiu wuzbong Normal school;one Results of the Diophantine Eqation in Continuous Integer[J];Journal of Anshun Teachers College;1995-02
9 Zhang Zhijun Wang Liying (Baicheng Normal College 137000);On Pell Equation[J];Journal of Baicheng Teachers College;2004-04
10 LIU Jing-xian (Development Planning Commission of Binzhou City, Binzhou 256602,China);Theorems of Structrue Solutions to Dyadic and Square Exponents Nondeterministic Equations[J];Journal of Binzhou Teachers College;2004-04
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 Luo Ming(Chongqing Teachers Colleg);Onthe Indeterminate Equation x3±1 = 14y2[J];JOURNAL OF CHONGQING JIAOTONG INSTITUTE;1995-03
2 Luo Ming (Department of Mathematics);ON THE DIOPHANTINE EQUATION X(X + 1 )(X + 2)(X + 3) = 7Y(Y + 1 )(Y + 2)(Y + 3)[J];Journal of Chongqing Teachers College(Natural Science Edition);1991-01
3 FENG Guo-feng~(1,2)(1.College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047;2.Dept.of Basic Instruction,Chongqing Vocational & Technical College,Chongqing 400712,China);On the Diophantine Equation x~3+1=2py~2[J];Journal of Chongqing Normal University(Natural Science Edition);2006-04
4 CHENG Yao,MA Yu-lin(College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China);The Diophantine Equation x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)[J];Journal of Chongqing Normal University(Natural Science Edition);2007-03
5 LIN Li-Juan1,HE Bo2(1.College of Mathematics and Computer,Chongqing Normal University,Chongqing 400047; 2.Longchang Xiangshi Middle School,Longchang Sichuan 642152,China);On the Diophantine Equation x~2-3y~4=22[J];Journal of Chongqing Normal University(Natural Science Edition);2007-03
6 Luo Ming(Dept.of Mathematics,Chongqing Teachers College,Chongqing,630047);On the Diophantine Equation x ̄4-pqy ̄2=1[J];JOURNAL OF CHONGQING TEACHERS COLLEGE(NATURAL SCIENCE EDITION);1995-03
7 Luo Ming(Dept. of Mathematics,Chongqing Teachers College,Chongqing,630047);On the Diophantine Equation x ̄3±8=7y ̄2[J];JOURNAL OF CHONGQING TEACHERS COLLEGE(NATURAL SCIENCE EDITION);1995-03
8 DUAN Hui-ming(School of Computer Science and Technology,Chongqing University of Post and Telecommunications,Chongqing 400065,China);On the Diophantine equation x~3+1=86y~2[J];Journal of Science of Teachers' College and University;2007-02
9 ZHOU Ke (Dept.of Mathematics and Computer Science of Cuangxi Teachers College,Nanning Guangxi 530001, China);About the Diophantine Equations x~4+m~y 4=nz~2[J];Journal of Guangxi Teachers College;2001-02
10 Zou Qing;ON THE NON-DETERMINISTIC EQUATION x~3±1=Dy~2[J];Journal of Hubei Agricultural College;1986-01
【Secondary References】
Chinese Journal Full-text Database 5 Hits
1 QU Yun-yun, BAO Xiao-minSchool of Mathematics and Statistics,Southwest University,Chongqing 400715,China;On the Diophantine Equation x~3+1=119y~2[J];Journal of Southwest China Normal University(Natural Science Edition);2009-01
2 LI Xin, LIANG Yan-huaSchool of Mathematics and Statistics,Southwest University,Chongqing 400715,China;The Diophantine Equations x~3-1=111y~2[J];Journal of Southwest China Normal University(Natural Science Edition);2009-01
3 GAN Xin-rong1,GAN Quan2,YAO Zhao-dong3 1.College of Sciences,Wuhan University of Science & Technology,Wuhan 430065;2.School of Electronic Information Wuhan University,Wuhan 430079;3.Air Force Radar Faculty,Wuhan 430019;Discussing Integer Solution of Non-degenerate Equation Again[J];Journal of Southwest China Normal University(Natural Science Edition);2009-03
4 Liu Jie(Sanming Vocational and Technical College,Sanming 365000,China);On the Diophantine Equation x~3+1=37y~2[J];Journal of Yunnan Nationalities University(Natural Sciences Edition);2008-04
5 LIU Jie (Sanming Vocational and Technical College,Fujian,Sanming 365000,China);On the Diophantine Equation x~3+1=129 y~2[J];Journal of Zhangzhou Normal University(Natural Science);2008-03
【Secondary Citations】
Chinese Journal Full-text Database 2 Hits
1 Chao Ko;ON THE D1OPHANTINE EQUATION x~2=y~n+1,xy≠0.[J];Journal of Sichuan University (Natural Science Edition);1962-01
2 Ko Chao Sun Chi;ON THE DIOPHANTINE EQUATIONSx~3+1=3Dy~2[J];Journal of Sichuan University (Natural Science Edition);1981-02
©2006 Tsinghua Tongfang Knowledge Network Technology Co., Ltd.(Beijing)(TTKN) All rights reserved