| 椭圆曲线y2=x3-17x+114的正整数点 |
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| 引用本文： | 赵建红 杜先存. 椭圆曲线y2=x3-17x+114的正整数点[J]. 西南师范大学学报(自然科学版), 2018, 43(4): 11-14 |
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| 作者姓名： | 赵建红 杜先存 |
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| 作者单位： | 丽江师范高等专科学校教师教育学院;红河学院教师教育学院 |
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| 摘 要： | 利用唯一分解定理、同余的性质、Legendre符号的性质、奇偶数的性质、Pell方程的解的性质等初等方法证明了椭圆曲线y~2=x~3-17x+114无正整数点.
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| 关 键 词： | 椭圆曲线 正整数点 Pell方程 同余 Legendre符号 |
On Positive Integral Points on Elliptic Curve y2=x3-17x+114 |
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| ZHAO Jian-hong DU Xian-cun. On Positive Integral Points on Elliptic Curve y2=x3-17x+114[J]. Journal of southwest china normal university(natural science edition), 2018, 43(4): 11-14 |
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| Authors: | ZHAO Jian-hong DU Xian-cun |
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| Affiliation: | Department of Teachers Education, Lijiang Teachers College; College of Teachers Education, Honghe University; |
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| Abstract: | In this paper, we are to prove the elliptic curve y2=x3-17 x+114 has no positive integer points by the unique decomposition theorem, some properties of congruence, Legendre symbols, odd and even number, solution of the Pell equation. |
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| Keywords: | elliptic curve positive integer point Pell equation congruence Legendre symbols |
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