| 不定方程组x~2-10y~2=1,y~2-Dz~2=4 |
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| 引用本文： | 冉延平.不定方程组x~2-10y~2=1,y~2-Dz~2=4[J].延安大学学报(自然科学版),2012,31(1):8-10. |
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| 作者姓名： | 冉延平 |
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| 作者单位： | 天水师范学院数学系,甘肃天水,741001 |
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| 基金项目： | 甘肃省校内基金(TSB0713) |
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| 摘 要： | 设D是无平方因子的偶数且D=2Πki=1piΠlj=1qj,pi=3,11,13,17,19,23,29,31,37（mod40）,qj=3,7,11,19,23,31（mod40）,或qj=1,5,13,17,19,29,37（mod40）,l≤3,其中诸pi,qj是互异奇素数,本文证明了不定方程组x2-10y2=1,y2-Dz2=4仅有非凡解D=2,（x,y,z）=（19,6,4）。
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| 关 键 词： | 不定方程组 pell方程 非平凡解 素因数 |
Integer Solution of the Simultaneous Diophantine Equations x~2-10y~2=1 and y~2-Dz~2=4 |
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| RAN Yan-ping.Integer Solution of the Simultaneous Diophantine Equations x~2-10y~2=1 and y~2-Dz~2=4[J].Journal of Yan'an University(Natural Science Edition),2012,31(1):8-10. |
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| Authors: | RAN Yan-ping |
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| Institution: | RAN Yan-ping(Department of Mathematics,Tianshui Normal University,Tianshui 741001,China) |
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| Abstract: | The following conclusion is proved:If D is an even square-free integer,D=2 Πk i=1 pi Πl j=1 qj,pi≡3,11,13,17,19,23,29,31,37(mod40),qj≡3,7,11,19,23,31(mod40),或qj≡1,5,13,17,19,29,37(mod40),l≤3,where pi,qj are different odd prime,then the equations in title only have a non-trivial solution D=2,(x,y,z)=(19,6,4). |
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| Keywords: | simultaneous diophantine equations pell equation non-trivial solution prime factors |
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