《数根丛草》注记

Notes on Shugen Congcao

李善兰《考数根法(》1872)与方士《数根丛草》(1897)是晚清讨论素数判别法的两部主要著作。解读两书内容,考察《数根丛草》对因数分解判别素数法的运用以及对《考数根法》求"定次"方法的完善等两项工作,可以看出晚清数学家对于费尔马小定理与费尔马因数分解判别素数法的深刻认识与灵活运用。此外,改正了以往关于《数根丛草》内容解释的一些错误和遗漏,并认为《考数根法》与《数根丛草》的内容与数学方法的来源需要进一步探讨。

Devoted to examine whether a number is a prime or not, Kao Shugen Fa （Prime Test,1872） of Li Shanlan and Shugen Congcao （Sequel to the Prime Test,1897） of Fang Shirong have ranked high in the history of mathematics in the late Qing Dynasty. Based on the texts of the two books,this paper lays stress on the investigation on factorization method for applying and Li＇s method for finding exponent completing that appeared in Fang＇s book. The result shows that mathematicians in the late Qing Dynasty had gained better appreciation of the little Fermat theorem and Fermat＇s fac- torization method. Some mistakes and omissions, which appeared in papers published in past years, have been corrected in the paper. The paper considers it necessary to inquire further into the origin of contents and mathematical method appearing in the two books.