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## On the Indefinite Equation x~3±1=2py~2

DU Xian-cun①,ZHAO Dong-jin②,ZHAO Jin-e③(①Teachers'Educational College;②College of Engineering;③Deparment of Mathematics,Honghe University,661199,Mengzi,Yunnan,PRC)
Let p be an odd prime of the form 6k+1.The sufficient conditions are obtained that indefinite equation x3±1=2py2 have no integer solutions by using the elementary method.
【Fund】： 云南省教育厅科研基金(2011C121)
【CateGory Index】： O156
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 【Citations】
 Chinese Journal Full-text Database 6 Hits
 1 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 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 ZHANG Shu-jing,YUAN Jin(Department of Mathematics,Northwest University,710127,Xi'an,Shannxi,PRC);On the Diophantine Equation x~3±1=Dy~2[J];Journal of Qufu Normal University(Natural Science);2009-04 4 HUANG Shou-sheng (Department of Mathematics,Maoming College,Guangdong 525000,China);On the Diophantine Equation x~3-1=2py~2[J];Journal of Mathematical Research and Exposition;2007-03 5 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 6 DU Xian-cun1,SHI Jia-yin2,ZHAO Jin-e3(1.School of Teacher’s Education,Honghe University,Mengzi 661199,P.R.C.;2.School of Arts and Culture,Yunnan Arts University,Kunming 650033,P.R.C.;3.Department of Mathematics,Honghe University,Mengzi 661199,P.R.C.);On the indefinite equation x~3-1=py~2[J];Journal of Southwest University for Nationalities(Natural Science Edition);2012-05
 【Co-citations】
 Chinese Journal Full-text Database 10 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 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 3 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 4 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 5 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 6 WANG Yun-kui WANG Jian-ping 1 (Department of Mathematics and Computer Science,Guangxi University for Nationalities,Nanning Guangxi,530006) (1 Center for Polytechnic Training,Guigang Guangxi,537100);ON THE DIOPHANTINE EQUATIONS x~6±y~6=Dz~2[J];Journal of Changde Teachers University;2001-02 7 WANG Yun-kui 1 LUO Yi-kui 2 (1.Guangxi University for Nationalities, Nanning Guangxi,530006); (2.Guangxi Jidian Vocatioral College, Nanning Guangxi,530007);ON THE TIJDEMAN CONJECTURE (Ⅰ)[J];Journal of Changde Teachers University;2002-04 8 XIONG Chuan,LUO Ming(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China);On the Diophantine Equation x~3+27=139y~2[J];Journal of Chongqing Normal University(Natural Science);2012-02 9 WANG Yun kui,LI Shu xin(Department of Mathematics and Computer Science,Guangxi University for Nationalities,Nanning 530006,China);On the Diophantine Equation x~3+y~3=Dz~2[J];Journal of Changsha Railway University;2002-01 10 Li Fuzhong (Department of Mathmatics,Northeast Normal University,Changchun,130024);On the Diophantine Equation x￣3±(2￣(2k-1))￣3=Dy￣2[J];JOURNAL OF NORTHEAST NORMAL UNIVERSITY (NATURAL SCIENCE EDITION);1994-04
 【Secondary Citations】
 Chinese Journal Full-text Database 10 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 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 3 Ni Guyan (Department of Systems Engineering and Mathematics, NUDT, Changsha, 410073);On The Diophantine Equation x 3=Dy 2+1[J];JOURNAL OF NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY;1999-05 4 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 5 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 6 x~3+1=Dy~2Ni Guyan(National University of Defence Technology);ON THE INDEFINITE EQUATIONS[J];NATURAL SCIENCE JOURNAL OF HARBIN NORMAL UNIVERSITY;1999-03 7 Yang Lifen; Hao Lizhu(Harbin Univ. of Civil Eng. and Arch.) (Dept. of Maths Heilonjiang Univ.);ON THE DIOPHANTINE EQUATION X￣3+1=DY￣2[J];NATURAL SCIENCE JOURNAL OF HARBIN NORMAL UNIVERSITY;1995-04 8 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 9 HAN Yun-na (Department of Mathematics,Northwest University,Xi`an 710127,P. R. China);On the Diophantine Equation x~3-1 =3py~2[J];Science Technology and Engineering;2010-16 10 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
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