一次同余式组的欧拉解法和黄宗宪反乘率新术

该文着重于用初等数论方法严格核对黄宗宪的反乘率新术，指出它同欧拉的一个一次同余式组解法是一致的，尽管在时间上晚于欧拉，但思路有所不同。黄宗宪是从研究改进秦九韶的大衍求一术出发，得到反乘率概念，再独立研究出反乘率新术，在计算上更体现出传统数学的算法化倾向。

EULER'S SOLUTION AND HUANG ZONGXIAN'S NEW METHOD WITH THE OPPOSITE MULTIPLYING TERM FOR LINEAR CONGRUENCES

This paper examines the new method with the opposite multiplying term for linear congruences by Huang Zongxian, and compares it with one of Euler's solutions. The paper shows that it is based on improving Qin Jiushao's method of seeking unity that Huang proposed the concept of the opposite multiplying term and developed independently his new method, which reflects the algorithmical tendency of traditional Chinese mathmatics.