| 李善兰《考数根法》研究 |
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| 引用本文： | 张必胜,姚远.李善兰《考数根法》研究[J].井冈山大学学报（自然科学版）,2011(4):25-29. |
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| 作者姓名： | 张必胜 姚远 |
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| 作者单位： | 西北大学数学系;西北大学数学与科学史研究中心; |
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| 基金项目： | 国家自然科学基金项目(10771169); 国家社会科学基金项目(07XXW004) |
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| 摘 要： | 基于李善兰考数根法原始文献的解读,将其解译为素数判定的数学定理,并表述为完整的现代数学符号语言。认为其等价于费马小定理,其素数判定的方法可解析为：屡乘求一、天元求一、小数回环、准根分级4种方法,进而将其具体分解为减少结算量而求定次d,李善兰给出了素数判定的充分必要条件。
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| 关 键 词： | 考数根法 李善兰（1811—1882） 素数 费马小定理 |
RESEARCH ABOUT 'KAO SHUGEN LAWS' OF LI SHAN-LAN |
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| ZHANG Bi-sheng,YAO Yuan.RESEARCH ABOUT 'KAO SHUGEN LAWS' OF LI SHAN-LAN[J].Journal of Jinggangshan University(Natural Sciences Edition),2011(4):25-29. |
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| Authors: | ZHANG Bi-sheng YAO Yuan |
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| Institution: | ZHANG Bi-sheng1,2,YAO Yuan1,2(1.Department of Mathematics,2.Research center for the History of Mathematics and Science,Northwest University,Xi'an,Shanxi 710127,China) |
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| Abstract: | Based on interpretation original documents about the kao shugen laws of Li Shan-lan,which is interpreted as the mathematical theory of prime numbers,and expressed as a complete language of modern mathematical symbols.It is equivalent to Fermat's small theorem.Its mathematical judgment methods of prime numbers be classified:nu-cheng find one method,tian-yuan find one method,xiao-shu loop back method,quasi-root classification method,then reduce the amount to break for the sake of its specific set times d,ulti... |
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| Keywords: | kao shugen laws Li Shan-lan prime numbers Fermat's small theorem |
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