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《Pure and Applied Mathematics》 2010-04
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On the Diophantine equation x~3+1 = py~2

GAO Jie 1,YUAN Jin 2(Department of Mathematics,Northwest University,Xi'an 710127,China)  
Using elementary theory of numbers methods,a sufficient condition is obtained that the Diophantine equation x3+1 = py2 has no positive integer solution,where p = 3(8t+4)(8t+5)+1 and p = 3(8t+3)(8t+4)+1.And get countless p,where p is an odd prime of the form 6k+1,meet the equation x3+1 = py2 without positive integer solution.
【CateGory Index】: O156.7
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【Citations】
Chinese Journal Full-text Database 6 Hits
1 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
2 YANG YA-lin(Department of Mathematics,Northwest University,Xi'an 710127,China);On the Diophantine equation x~3+1=py~2[J];Journal of Science of Teachers' College and University;2008-05
3 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
4 Wang Chunyan Tian Xiaoxia(School of Mathematics and Statistics,Southwest University,Chongqing,400715);On the Diophantine Equations x-1=3py~2,x~2+x+1=3z~2[J];Mathematical Theory and Applications;2008-04
5 Ko Chao Sun Chi;ON THE DIOPHANTINE EQUATIONSx~3+1=3Dy~2[J];Journal of Sichuan University (Natural Science Edition);1981-02
6 MU Quan-wu,WU QiangSchool of Mathematics and Statistics,Southwest University,Chongqing 400715,China;On the Diophantine Equation x~3-1=103y~2[J];Journal of Southwest University(Natural Science Edition);2008-10
【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 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
6 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
7 Ji wanhui Ning Xiu wuzbong Normal school;one Results of the Diophantine Eqation in Continuous Integer[J];Journal of Anshun Teachers College;1995-02
8 Zhang Zhijun Wang Liying (Baicheng Normal College 137000);On Pell Equation[J];Journal of Baicheng Teachers College;2004-04
9 LE Mao-hua(Department of Mathematics,Zhanjiang Normal College,Zhanjiang Guangdong,524048,P.R.China);On the Diophantine Equation x~3+1=3py~2[J];Journal of Baoding Teachers College;2004-02
10 LE Mao-hua~(1,2) (Dept.Math., Zhanjiang Normal College, Zhanjiang 524048,Guangdong, China; Dept. Math. Wuzhou Normal School, Hezhou 542800, Guangxi, China);On the Diophantine equation x~3-1=py~2[J];Journal of Baoji College of Arts and Science(Natural Science Edition);2004-02
【Secondary Citations】
Chinese Journal Full-text Database 10 Hits
1 LUO Ming (College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047,China);On the Diophantine Equation x~3+1=7y~2[J];Journal of Chongqing Teachers College(Natural Science Edition);2003-01
2 LE Mao-hua (Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,China);On the Diophantine Equation x~3+1=py~2[J];Journal of Guangxi Teachers Education University(Natural Science Edition);2005-04
3 Mu Shanzhi Li Tongjun (Harbin University of Technology);Solution on the Diophantine Coupled Equations[J];Journal of Hebei Institute of Mechano-Electric Engineering;1996-04
4 DUAN Hui-ming,ZHU Guo-hui (Dept. of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China);On the Diophantine Equation x~3-1=38y~2[J];Journal of Huanggang Normal University;2005-03
5 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
6 Pan Jiayu (Department of Basic Sciance, Zhengzhou Grain college) Zhengzhou 450052;ON THE DIOPHANTINE EQUATIONS x 3±1=Dy 2[J];HENAN SCIENCE;1997-04
7 Ko Chao Sun Chi;ON THE DIOPHANTINE EQUATIONSx~3+1=3Dy~2[J];Journal of Sichuan University (Natural Science Edition);1981-02
8 Ko Chao Snn Chi;ON THE DIOPHANTINE EQUATIONS x3 +8 =Dy2AND X3+ 8=3Dy2[J];Journal of Sichuan University (Natural Science Edition);1981-04
9 MU Quan-wu (School of Mathematics and Statistics,Southwest China University,Chongqing 400715,China);A Note on "On the Diophantine Equation x~3-1=2py~2"[J];Journal of Xi'an University of Arts & Science(Natural Science Edition);2008-04
10 LUO Ming1, HUANG Yong-qing21.School of Mathematics and Statistics,Southwest University,Chongqing 400715,China;2.College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China;On the Diophantine Equation x~3-1=26y~2[J];Journal of Southwest University(Natural Science Edition);2007-06
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