| 一类Diophantine方程及其他的整数解 |
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| 引用本文： | 赵院娥.一类Diophantine方程及其他的整数解[J].西北大学学报,2012(4):533-535. |
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| 作者姓名： | 赵院娥 |
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| 作者单位： | 延安大学数学与计算机学院 |
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| 基金项目： | 国家自然科学基金资助项目(11071194);陕西省教育厅自然科学计划基金资助项目(11JK0489) |
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| 摘 要： | 目的研究不定方程x3±8=Dy2的可解性问题。方法利用初等及代数方法。结果设D是不含3和6k+1之形素因数的无平方因子正整数。当D>5时,如果D的素因数p都满足p≡1,3(mod 8)或者p≡5,7(mod 8),则方程x3±8=Dy2没有适合gcd(x,y)=1的正整数解(x,y)。结论部分地解决了该方程的可解性问题。即对某些特殊D,该方程无解。
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| 关 键 词： | 三次Diophantine方程 正整数解 同余条件 |
One kind Diophantine equation and its integer solutions |
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| ZHAO Yuan-e.One kind Diophantine equation and its integer solutions[J].Journal of Northwest University(Natural Science Edition),2012(4):533-535. |
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| Authors: | ZHAO Yuan-e |
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| Institution: | ZHAO Yuan-e(College of Mathematics and Computer Science,Yan′an University,Yan′an 716000,China) |
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| Abstract: | Aim To study the solvability of the Diophantine equation x3±8=Dy2.Methods The elementary and algebra methods.Results Let D be a positive integer such that 3×D,D is square free and D has no prime divisor with form 6k+1.If D>5 and every prime divisor p of D satisfies either p≡1,3(mod 8) or p≡5,7(mod 8),then the equation x3±8=Dy2 has no positive integer solution(x,y) with gcd(x,y)=1.Conclusion It is proved that the Diophantine equation has not integer solutions for some special integers D. |
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| Keywords: | cubic Diophantine equation positive integer solution congruence condition |
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