| 引用本文： |
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高丽,鲁伟阳,郝虹斐.不定方程x3+1=301y2的整数解[J].广西科学,2014,21(3):290-292. [点击复制]
- GAO Li,LU Wei-yang,HAO Hong-fei.The Integral Solutions of Diophantine Equation x3+1=301y2[J].Guangxi Sciences,2014,21(3):290-292. [点击复制]
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| 摘要: |
| 利用递归数列、同余式、平方剩余以及Pell方程解的性质证明不定方程x3+1=301y2仅有整数解(x,y)=(-1,0). |
| 关键词: 不定方程 整数解 递归数列 同余式 |
| DOI：10.13656/j.cnki.gxkx.20140414.001 |
| 投稿时间：2013-03-30修订日期：2013-06-05 |
| 基金项目:国家自然科学基金项目(10271093),陕西省教育厅自然科学基金项目(2013JQ1019),延安大学高水平大学建设项目(2012SXTS07),延安大学自然科学专项科研基金项目(YDZ2013-04),延安大学硕士研究生教育创新计划项目资助。 |
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| The Integral Solutions of Diophantine Equation x3+1=301y2 |
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GAO Li, LU Wei-yang, HAO Hong-fei
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| (College of Mathematics and Computer Science, Yan'an University, Yan'an, Shaanxi, 716000, China) |
| Abstract: |
| In this paper, the author used recurrent sequence, congruence sequence, quadratic remainder and some properties of the solutions to Pell equation to prove that the Diophantine equation x3+1=301y2 has only integer solution (x, y)=(-1, 0). |
| Key words: diophantine equation integer solution recurrent sequence congruence sequence |
