初等数论在历史年代学中的应用

The Application of Elementary Number Theory in the Historical Chronology

应用初等数论中的同余式、连分数、渐近分数、不定方程等工具,分析考古年代学提出的若干问题,以敦煌汉简、居延汉简、《史记》等出土文物和史料为证据,将《二十史朔闰表》、《三千五百年历日天象》的记录视为大时段日月运行的数据库,证明或论述中国历法的五个周期性质,从而阐明应用数学进行年代考释的基本原理和方法。

Based on some tools in elementary number theory, such as congruence, asymptotic fraction, the continued fraction Diophantine equation, etc., this paper analyzes some questions presented in archaeological chronology. Taking Dunhuang bamboo slips, Ju Yan bamboo slips of Han Dynasty, the book 'Historical Records', unearthed relics and historical data as evidence, and the records of 'Calendar of Twenty Dynasties in China'and'Calendar in Three Thousand Five Hundred Years'as a database of sun and moon movements,this paper proves and discusses five cycles properties in Chinese calendar so as to clarify the basic principles and methods of the archaeological chronology of mathematics.