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《Journal of Changsha University》 2013-05
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On the Diophantine Equation x~3- 8 = Dy~2

WAN Fei;DU Xiancun;College of Teachers' Education,Honghe University;  
Let D be an odd prime of the form 6k + 1.With the elementary method,it is proved that the Diophantine equation x3-8 = Dy2(x,y ∈N) has no integer solutions with gcd(x,y) = 1,when D = 12k(4k-1) + 1(k ∈Z+).
【CateGory Index】: O156.7
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【Citations】
Chinese Journal Full-text Database 5 Hits
1 Cao Yushu(Dept. of Maths., Heilongjlang Univ.);On the Diophantine Equation x~3±8 = 3Dy~2[J];Journal of Natural Science of Heilongjiang University;1991-01
2 Cao Yushu Huang Longxiang(Dept. of Maths Heilongjiang Univ.)(Dept of Maths Heilongjiang Farm Teacher's College);On The Diophantine Equation x~3±8=Dy~2[J];Journal of Natural Science of Heilongjiang University;1992-02
3 LEMao-hua (Department of Mathematics, Zhanjiang Normal College,Zhanjiang 524048,China; Department of Mathematics,Wuzhou Teachers College,Hezhou 542800,China);On the Diophantine equation x~3-8=py~2[J];Yantai Normal University Journal(Natural Science);2004-03
4 LE Mao-hua(School of Mathematics and Computational Science, Zhanjiang Normal College, Zhanjiang,Guangdong 524048,P.R.China);On the Diophantine Equation x~3-8=3py~2[J];Journal of Zhanjiang Teachers College;2004-03
5 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 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
4 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
5 Li Fuzhong(Department of Mathematics, Northeast Normal University, Changchun,130024);On the Diophantine Equation x ̄3±512=3Dy ̄2[J];JOURNAL OF NORTHEAST NORMAL UNIVERSITY (NATURAL SCIENCE EDITION);1994-01
6 Li Fuzhong(Department of Mathematics. Northeast Normal University,Changchun. 130024);On the Diophantine Equation x ̄3±64=3Dy ̄2[J];JOURNAL OF NORTHEAST NORMAL UNIVERSITY (NATURAL SCIENCE EDITION);1994-02
7 YANG YA-lin1,2 (1.Weinan Senior Middle School,Weinan,Shaanxi 714000,China; 2.Department of Mathematics,Northwest University,Xi′an 710127,China);On the Diophantine equation x~3-8=py~2[J];Basic Sciences Journal of Textile Universities;2010-03
8 LI Ya-zhuo(Department of Journal Publishing,Shaanxi Institute of Education,Xi’an 710061,China);On the Diophantine equation x~3+1=py~2[J];Journal of Science of Teachers' College and University;2011-01
9 CUI Bao-jun(Department of Mathematics,Gansu Normal University for Nationalities,Hezuo 747000,China);The solutiont of Diophantine equation x~3-8=65y~2[J];Journal of Science of Teachers' College and University;2012-01
10 CUI Bao-jun(Department of Mathematics,Gansu Normal University for Nationalities,Hezuo Gansu 747000);On the Diophantine Equation x~3-8=65y~2[J];Journal of Gansu Normal Colleges;2012-02
【Secondary Citations】
Chinese Journal Full-text Database 7 Hits
1 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
2 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
3 Cao Yushu, Guo Qingjiang;On the Diophantine Equation x~3±1=3Dy~2[J];Journal of Natural Science of Heilongjiang University;1989-04
4 Cao Yushu(Dept. of Maths., Heilongjlang Univ.);On the Diophantine Equation x~3±8 = 3Dy~2[J];Journal of Natural Science of Heilongjiang University;1991-01
5 Cao Yushu Huang Longxiang(Dept. of Maths Heilongjiang Univ.)(Dept of Maths Heilongjiang Farm Teacher's College);On The Diophantine Equation x~3±8=Dy~2[J];Journal of Natural Science of Heilongjiang University;1992-02
6 LEMao-hua (Department of Mathematics, Zhanjiang Normal College,Zhanjiang 524048,China; Department of Mathematics,Wuzhou Teachers College,Hezhou 542800,China);On the Diophantine equation x~3-8=py~2[J];Yantai Normal University Journal(Natural Science);2004-03
7 HE Bo (Xiangshi Middle School, Longchang, Sichuan 642152, P.R.C.);On the Diophantine equation x~3-1 = 61y~2[J];Journal of Southwest University for Nationalities (Natural Science Edition);2004-06
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