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一 引言 勾股定理是一个古老而又有益的问题。据《周髀算经》载有荣方与陈子关于测量太阳离地面高度的对话,可知中国学者陈子早在公元前七～六世纪,就掌握了直角三角形三边间的关系。据传,同时期的古希腊的毕达哥拉斯(Pythagoras)从理论上证明了该定理。大约到了公元250年前后,丢番图(Diophantos)开始将确定整数边长的直角三角形问题转化为与之等价的确定方程x~2+y~2=z~2的正整数解(今天称之为勾股数)的求解问题.公元600年左右,
I. INTRODUCTION The Pythagorean theorem is an old and useful question. According to the Zhouyi Sutra, which contains dialogues between Rong Fang and Chen Zi on measuring the height of the sun from the ground, it can be known that the Chinese scholar Chen Zi had mastered the relationship between the three sides of a right-angled triangle from the 7th to the 6th century BC. According to legend, Pythagoras of ancient Greece proved this theorem theoretically. About around AD 250, Diophantos began to convert the right-angled triangular problem that determined the length of an integer into a positive integer solution to the equivalent deterministic equation x~2+y~2=z~2. For the problem of solving the number of shares. The year around 600 AD,