| 一类无非平凡有理整点的椭圆曲线y~2=x(x-p)(x-q) |
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| 引用本文： | 李斐.一类无非平凡有理整点的椭圆曲线y~2=x(x-p)(x-q)[J].首都师范大学学报(自然科学版),2014(2):5-6. |
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| 作者姓名： | 李斐 |
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| 作者单位： | 安徽财经大学统计与应用数学学院; |
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| 摘 要： | 令p、q为两个素数,且p+4=q。本文证明了椭圆曲线y2=x(x-p)(x-q)没有非平凡有理整点.同时得到了一类无整解的负Pell方程组和一类无整解的四次丢番图方程.
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| 关 键 词： | 椭圆曲线 有理整点 丢番图方程. |
A Type of Elliptic Curves y～2= x（ x-p）（ x-q） with no Nontrivial Integer Points |
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| Li Fei.A Type of Elliptic Curves y～2= x（ x-p）（ x-q） with no Nontrivial Integer Points[J].Journal of Capital Normal University(Natural Science Edition),2014(2):5-6. |
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| Authors: | Li Fei |
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| Institution: | Li Fei (School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, Anhui,233030) |
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| Abstract: | It is shown that the type of elliptic curves y2= x（ x- p）（ x- q） have no nontrivial integer points,provided the two primes p and q satisfy p ＋ 4 = q. Based on this,we get a type of simultaneous negative Pell equations and a type of quartic Diophantine equations,which have no solutions either. |
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| Keywords: | elliptic curve integer point Diophantine equation |
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