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《Journal of Wuhan University(Natural Science Edition)》 1990-01
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THE INTEGER SOLUTION OF THE SIMULTANEOUS EQUATIONS x~2-2y~2=1 AND y~2-Dz~2=4

Chen jianhua (Department of mathematics,Wuhan University)  
In this paper,the simultaneous equations(1) x~2-2y~2=1 y~2-Dz~2=4(1) is considered,we completely solve the equations(1)when D=p or pq,here p,q are odd primes,the only non-trivial integer solution(xyz≠0)of equations (1)is given by x=7,y=12,z=2 when p=5 and q=7.If we put D=5,we obtain the result proved by S.P.Mohanty and A.M.S.Ramasamy recently in J.Number Theory(18(1984),356-359)that the simultaneous equations(2) x~2-2y2=1 5y~2-z~2=20(2) have the only integer solution when z=0.
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1 YANG Shi-chun (Aba Teachers College,Wenchuan,Sichuan,623000,China);Some Results Concerning Odd Perfect Numbers of the Form N = π~α 3~(2β)Q~(2β)[J];Journal of ABA Teachers College;2006-04
2 YANG Shi-chun,WU Wen-quan (Math Dept.of Aba Teachers College,Wenchuan Sichuan 623000,China);Probes into "Low Starting Point and High Qualities" Curriculum Building Mode of Elementary Number Theory[J];Journal of ABA Teachers College;2007-03
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4 WU Xin-sheng (The 16th Electronic Research Institute of the Ministry of Information Industry, Hefei 230061,China);The Representation of Large Even Integer as a Sum of Two Primes[J];Journal of Anhui Tv University;2001-01
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【Co-references】
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1 CHEN Xi geng 1,LE Mao hua 2(1.Department of Mathematics,Maoming College,Maoming 525000,China;2.Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,China);Square classes of generalized Pell sequences[J];Journal of Foshan University(Natural Science Edition);2003-02
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3 HU Yong zhong, HAN Qing (Department of Mathematics, Foshan University, Foshan, Guangdong 528000);On the integer solution of the simultaneous equations x~2-2y~2=1 and y~2-Dz~2=4[J];Journal of Central China Normal University(Natural Sciences);2002-01
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1 LE Mao-hua Department of Mathematics, Zhanjiang Normal College,Zhanjiang 524048, China;On the simultaneous Pell equations x~2 - 4D_1y~2 = 1 and y~2-D_2z~2= 1[J];Journal of Foshan University(Natural Science Edition);2004-02
2 HU Yong zhong, HAN Qing (Department of Mathematics, Foshan University, Foshan, Guangdong 528000);On the integer solution of the simultaneous equations x~2-2y~2=1 and y~2-Dz~2=4[J];Journal of Central China Normal University(Natural Sciences);2002-01
3 LE Mao-hua (Dept. of Mathematics, Zhanjiang Normal College, Zhanjiang 524048, China);On the simultaneous Pell equations x~2-4D_1y~2 and y~2-D_2z~2=1[J];Journal of Jilin Institute of Chemical Technology;2004-01
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8 DONG Biao,YANG Shi-chun (ABa Teacher' s College , Wenchuan 623000, China );On the Integer Solution of Pell Equations x2-2y2=1,y2-Dz2=4[J];Journal of Beihua University(Natural Science);2003-02
9 WANG Guan-min,LI Bing-rong (Department of Mathematics, Zhangzhou Teachers College);The Integer Solution Of The Pell`S Equations x~2-6y~2=1 and y~2-Dz~2=4[J];Journal of ZhangZhou Teachers College;2002-04
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