| 关于Diophantine方程x~3+1=3py~2 |
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| 引用本文： | 贾晓明,牛莹莹. 关于Diophantine方程x~3+1=3py~2[J]. 高师理科学刊, 2009, 29(3) |
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| 作者姓名： | 贾晓明 牛莹莹 |
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| 作者单位： | 1. 西北大学,数学系,陕西,西安,710127
2. 西北工业大学,应用数学系,陕西,西安,710129 |
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| 摘 要： | 设p是奇素数,证明了当p=108 s2+1,其中s是正整数时,方程x 3+1=3py2无正整数解(x,y).
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| 关 键 词： | 三次Diophantine方程 正整数解 同余 递归数列 |
On the Diophantine equation x~3+1=3py~2 |
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| JIA Xiao-ming,NIU Ying-ying. On the Diophantine equation x~3+1=3py~2[J]. Journal of Science of Teachers＇College and University, 2009, 29(3) |
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| Authors: | JIA Xiao-ming NIU Ying-ying |
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| Affiliation: | 1.Department of Mathematics;Northwest University;Xi`an 710127;China;2.Department of Applied Mathematics;Northwestern Polytechnical University;Xi`an 710129;China |
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| Abstract: | Let p be an odd prime,proven that if p=108 s2+1,where s is an positive integer,then equation x3+1=3py2has no positive solutions. |
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| Keywords: | cubic diophantine equation positive integer solution congruence recursive series |
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