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## On the diuphantine equation x~3±1=py~2

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)
In the paper,we have proved the following theorem:(1) the Diuphantine equations x+1=3py21,x2-x+1=3y22,(y1,y2)=1,y10,y20,where p was an odd prime number,has no positive integer solution x,p,y1,y2.(2) the Diuphantine equation x3+1=py2,where p≡-1(mod 3) was an odd prime number,has only integer solution(x,y)=(-1,0).(3) the Diuphantine equation x3-1=py2,where p≡-1(mod 3) was an odd prime number,has only integer solution(x,y)=(1,0).
【CateGory Index】： O156.7 Download(CAJ format) Download(PDF format)
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 【References】
 Chinese Journal Full-text Database 5 Hits
 1 GAO Jie 1,YUAN Jin 2(Department of Mathematics,Northwest University,Xi'an 710127,China);On the Diophantine equation x～3+1 = py～2[J];Pure and Applied Mathematics;2010-04 2 He Tao,Guo Jinbao,Mu Xiumei,Zhao Xinhua(College of Mathematics and Computer Science,Yan'an University,Yan'an 716000,Shaanxi China);On the Diophantine Equation x~3-1=py~2[J];Henan Science;2011-12 3 GUAN Xun-gui(Mathematics & Physics of Taizhou Normal College,Taizhou Jiangsu 225300,China);On the Indefinite Equation x~3+1=py~2[J];Journal of Huaiyin Teachers College(Natural Science);2011-04 4 GAO Jie,LIANG Yong(Department of Mathematics, Northwest University, Xi’an 710127, P.R.China);On the Diophantine Equation x~3-1=py~2[J];Science Technology and Engineering;2010-18 5 CHEN Jinping(College of Mathematics and Information,China West Normal University,Nanchong 637002,Sichuan,China);On the Diophantine Equationx~3+1=7py~2[J];Journal of Zhanjiang Normal College;2012-03
 【Citations】
 Chinese Journal Full-text Database 4 Hits
 1 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 2 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 3 Ko Chao Sun Chi;ON THE DIOPHANTINE EQUATIONSx~3+1=3Dy~2[J];Journal of Sichuan University (Natural Science Edition);1981-02 4 Ko Chao Snn Chi;ON THE DIOPHANTINE EQUATIONS x3 +8 =Dy2AND X3+ 8=3Dy2[J];Journal of Sichuan University (Natural Science Edition);1981-04
 【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 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 4 ZHOU Wei-ping(Department of Mathematics and Computational Science,Anqing teachers College,Anqing,Anhui,246133,China);A Note on the Dionphantine Equation x~3+1=2py~2[J];Journal of Anqing Teachers College(Natural Science Edition);2010-01 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 TONG Rui-zhou1,WANG Zhen-tang2(1.Chaoyang Teachers College,Chaoyang 122000,China;2.Chaoyang School Finance,Chaoyang 122000,China);Study on Diophantine equation x~4-py~4=z~2[J];Journal of University of Science and Technology Liaoning;2011-02 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 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
 【Co-references】
 Chinese Journal Full-text Database 10 Hits
 1 Xuan Tizuo;THE DIOPHANTINE EQUATION Y(Y+1)(Y+2)(Y+3)=5X(X+1)(X+2)(X+3)[J];Journal of Beijing Normal University(Natural Science);1982-03 2 GAO Jie 1,YUAN Jin 2(Department of Mathematics,Northwest University,Xi'an 710127,China);On the Diophantine equation x～3+1 = py～2[J];Pure and Applied Mathematics;2010-04 3 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 4 Luo Ming(Chongqing Teachers Colleg);Onthe Indeterminate Equation x3±1 = 14y2[J];JOURNAL OF CHONGQING JIAOTONG INSTITUTE;1995-03 5 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 6 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 7 HUANG Yong-qing;LIAO Jiang-dong College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China;On the Diophantine Equation X~3±8=35y~2[J];Journal of Chongqing Nornal University(Natural Science Edition);2007-02 8 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 9 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 10 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
 【Secondary References】
 Chinese Journal Full-text Database 8 Hits
 1 DOU Zhi-hong(School of Mathematics and Statistics,Inner Mongolia Finance and Economics College,Hohhot 010051,China);The number of positive integral points on the elliptic curve y~2 = 2px(x~2 + 1)[J];Pure and Applied Mathematics;2011-02 2 GUAN Xun-gui(Mathematics & Physics of Taizhou Normal College,Taizhou Jiangsu 225300,China);On the Indefinite Equation x~3+1=py~2[J];Journal of Huaiyin Teachers College(Natural Science);2011-04 3 DU Xian-cuna,LI Yu-longa,ZHAO Jin-eb(a.Teachers' Educational College;b.Dept.of Mathematics,Honghe University,Mengzi 661199,China);Indefinite Equation x~3-1=Dy~2[J];Journal of Sichuan University of Science & Engineering(Natural Science Edition);2012-04 4 DU Xian-cun①,ZHAO Dong-jin②,ZHAO Jin-e③(①Teachers'Educational College;②College of Engineering;③Deparment of Mathematics,Honghe University,661199,Mengzi,Yunnan,PRC);On the Indefinite Equation x~3±1=2py~2[J];Journal of Qufu Normal University(Natural Science);2013-01 5 WAN Fei①,DU Xian-cun①,ZHAO Jin-e②(①Teachers’Educational College;②Department of Mathematics,Honghe University,661199,Mengzi,Yunnan,PRC);On the Exponent Diophantine Equation x~3+1=py~2 and x~3+1=3py~2[J];Journal of Qufu Normal University(Natural Science);2013-03 6 WAN Fei,DU Xian-cun(School of Teacher’s Education,Honghe University,Mengzi 661199,P.R.C.);On the Diophantine equation x~3-1=2py~2[J];Journal of Southwest University for Nationalities(Natural Science Edition);2012-05 7 CHEN Jinping(College of Mathematics and Information,China West Normal University,Nanchong 637002,Sichuan,China);On the Diophantine Equationx~3+1=7py~2[J];Journal of Zhanjiang Normal College;2012-03 8 DU Xiancun(Teachers'Educational College,Honghe University,Mengzi 661199,China);On indefinite equation x~3+1=Dy~2[J];Journal of Zhoukou Normal University;2013-02
 【Secondary Citations】
 Chinese Journal Full-text Database 1 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
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