| 关于Diophantine方程nx(x+d)(x+2d)(x+3d)=y(y+d)(y+2d)(y+3d)的一点注记 |
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| 引用本文： | 乐茂华. 关于Diophantine方程nx(x+d)(x+2d)(x+3d)=y(y+d)(y+2d)(y+3d)的一点注记[J]. 曲靖师范学院学报, 2009, 28(3) |
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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,广东,湛江,524048 |
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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d是大于1的正整数.本文运用初等数论方法证明了:如果d的素因数P都适合P=2或者p=±3(mod 8),则方程2x(x+d)(x+2d)(x+3d)=y(y+d)(y+2d)(y+3d))仅有正整数解(x,y)=(4d,5d).
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| 关 键 词： | 四次Diophantine方程 正整数解 二次非剩余 |
A Note on the Diophantine Equation nx(x+d)(x+2d)(x+3d)=y(y+d)(y+2d)(y+3d) |
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| Le Maohua. A Note on the Diophantine Equation nx(x+d)(x+2d)(x+3d)=y(y+d)(y+2d)(y+3d)[J]. Journal of Qujing Normal College, 2009, 28(3) |
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| Authors: | Le Maohua |
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| Affiliation: | Department of Mathematics;Zhanjiang Normal College;Zhanjiang Guangdong 524048;China |
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| Abstract: | |
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| Keywords: | quartic diophantine equation positive integer solution continued positive integers |
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