| 渐近分数的应用研究 |
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| 引用本文： | 杜丽英,杨中和,陈广锋.渐近分数的应用研究[J].西安文理学院学报,2011(3):34-36. |
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| 作者姓名： | 杜丽英 杨中和 陈广锋 |
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| 作者单位： | [1]西安建筑科技大学数学系,陕西西安710055 [2]西安文理学院数学系,陕西西安710065 |
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| 基金项目： | 西安建筑科技大学教改项目（JG080113） |
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| 摘 要： | 用渐近分数得到了两个结果：（1）用√n的渐近分数表示了纯循环二次无理数α=（α＋√n）／b的循环节所构成的分数，从而引出了用辗转相除法给出α的连分数的算法．（2）当A为合数时，用渐近分数给出了不定方程x^2-ny^2=±A的另一解法．
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| 关 键 词： | 连分数 循环节 渐近分数 |
A Study on the Application of Convergent |
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| DU Li-ying,YANG Zhong-he,CHEN Guang-feng.A Study on the Application of Convergent[J].Journal of Xi‘an University of Arts & Science:Natural Science Edition,2011(3):34-36. |
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| Authors: | DU Li-ying YANG Zhong-he CHEN Guang-feng |
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| Institution: | 1. Department of Mathematics, Xi＇ an University of Architecture ＆ Technology, Xi＇ an 710055 mChina; 2. Department of Mathematics, Xi＇an University of Arts ＆ Science, Xi＇an 710065, China) |
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| Abstract: | This study addresses convergent. The findings are as follows, （ 1 ） the convergent of √n represents the fraction composed by repetend of pure recurring quadratic irrational number α=（α＋√n）/b and arithmetic of continued fraction of ot is educed with method of successive division. （2） When A is a composite number, another solution of indeterminate equations x^2-ny^2=±A is given with convergent. |
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| Keywords: | continued fraction repetend convergent |
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