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《Journal of Mathematical Research and Exposition》 2007-03
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On the Diophantine Equation x~3-1=2py~2

HUANG Shou-sheng (Department of Mathematics,Maoming College,Guangdong 525000,China)  
Let p be an odd prime.This paper proves that ifp=48t~2+1,where t is a positive integer, then the equation x~3-1=2py~2 has no positive integer solution(x,y).
【Fund】: 国家自然科学基金(10271104);; 广东省自然科学基金(011781);; 茂名学院科研基金(203214).
【CateGory Index】: O156
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【References】
Chinese Journal Full-text Database 2 Hits
1 LIANG Yana,ZHOU Fangmin(Faculty of Mathematics and Information Sciences,Zhaoqing University,Zhaoqing Guangdong 526061,China);On the Diophantine Equation x~3-1=Dy~2[J];Journal of Zhaoqing University;2008-05
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【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 TIAN Xiao-xia,WANG Chun-yan(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China);On the Diophantine Equations x+1=6py~2,x~2-x+1=3z~2[J];Journal of Sichuan University of Science & Engineering(Natural Science Edition);2009-01
2 LIANG Yana,ZHOU Fangmin(Faculty of Mathematics and Information Sciences,Zhaoqing University,Zhaoqing Guangdong 526061,China);On the Diophantine Equation x~3-1=Dy~2[J];Journal of Zhaoqing University;2008-05
3 XIAO Qing-can (Department of Mathematics, Guangzhou Teachers College, Guangzhou 510405 China);ON the Diophantine Equation X~p - 1 = Dy~2[J];Journal of Biomathematics;2000-03
4 WANG Yan-qiu(School of Teachers,Hanzhong Vocational and Technical College,Hanzhong 723000,China);On the Diophantine equation x~3+1=26y~2[J];Journal of Shaanxi University of Technology(Natural Science Edition);2007-03
5 TANG Zong-ming(Suzhou College of Education,Tang zhongming,215002);On the Diophantine Equation x~3 ±5~6 =Dy~2[J];;2002-04
6 YANG Shi-chun (Aba Teachers College, Wenchuan Sichuan 623000, China);On the Diophantine Equation x~3±p~(3n)=Dy~2[J];Jourmal of Tianzhong;2003-05
7 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
8 PU Yan-yang , WANG Yun-kui (GuangxifangzhigongyeSchool, Nanning 530004, China; Dept. of Maths, Guangxi University for Nationalities, Nanning 530004, China);On the Diophantine x~2±xy+y~2 = k[J];;2003-04
9 LE Mao-hua (Department of Mathematics, Zhanjiang Normal College, Zhanjiang, Guangdong, 524048, China);ON THE DIOPHANTINE EQUATION x~3-1=Dy~n[J];Journal of Zhangzhou Vocational University;2005-01
10 LI Shuang-zhi, LUO Ming School of Mathematics and Statistics,Southwest University,Chongqing 400715,China;On the Diophantine Equation x~3+1=201y~2[J];Journal of Southwest China Normal University(Natural Science Edition);2010-01
【Co-references】
Chinese Journal Full-text Database 1 Hits
1 Ko Chao Snn Chi;ON THE DIOPHANTINE EQUATIONS x3 +8 =Dy2AND X3+ 8=3Dy2[J];Journal of Sichuan University (Natural Science Edition);1981-04
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