求解“韩信点兵”问题的算法研究

A Study on the Algorithm of Solving"Han Xin Calculate the Sum Total of Soldiers"Question

求解“韩信点兵”问题可归结为一次同余式组x≡ri，（modPi）或一次不定方程组x=pixi＋ri的求解。当方程的个数n与模pi（i=1，2，…，n）较大时，用同余式理论和孙子定理求解的过程非常繁琐。为此，运用试算分析法和辗转相除法，给出了求解上述问题的两种通用的计算机算法和程序。通过实践证明，该算法具有计算步骤简便，求解灵活快速，通用性强等优点。

The paper give out two kind of common computer algorithm and programof solving 'Han Xin calculate the sum tolal of soldiers' question nith trial calculation and analysis method and nutual division. Proved by practice,the algorithm is simple, flexible,and has the advantage of quick speed,strong generality and etc.