| 孪生素数椭圆曲线E_+的整数点 |
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| 引用本文： | 乐茂华.孪生素数椭圆曲线E_+的整数点[J].云南师范大学学报(自然科学版),2010,30(6). |
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| 作者姓名： | 乐茂华 |
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| 作者单位： | 湛江师范学院数学系; |
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| 基金项目： | 国家自然科学基金，广东省自然科学基金 |
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| 摘 要： | 设p和q是适合p+2=q的孪生素数.文章根据二元四次Diophantine方程和联立Pell方程组的解数上界证明了:当p≡1(mod 4)时,椭圆曲线E+:y2=x(x+p)(x+q)没有非平凡整数点(x,y);当p3且p≡3(mod 4)时,E+至多有3对非平凡整数点.
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| 关 键 词： | 孪生素数椭圆曲线 整数点 Diophantine方程 |
lntegral Points on Twin Prime Elliptic Curve E+ |
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| Le Mao-hua.lntegral Points on Twin Prime Elliptic Curve E+[J].Journal of Yunnan Normal University (Natural Sciences Edition),2010,30(6). |
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| Authors: | Le Mao-hua |
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| Institution: | Le Mao-hua (Department of Mathematics,Zhanjiang Normal College,Zhanjiang,Guangdong 524048,P.R.China) |
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| Abstract: | Let p and q be twin primes with p+2=q.Using some upper bounds for solutions of quartic diophantine equations and simultaneous Pell equations,we prove that if,then the elliptic curve has no non-trivial integral point;if p>3 and,then E+ has at most three pairs of non-trivial integral points. |
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| Keywords: | twin prime elliptic curve integral point diophantine equation |
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