摘要
本文将一个数学竞赛题的证明,归结为整数变量的多元平方和函数的最小值问题的求解,这些变量的和等于一个整数常数,这样的函数的最小值,及最大值的问题,则是更重要的离散数学问题,本文对此问题的求解,建立了完整的理论,并给出了一般的解法。
This article, concerning the proof of a mathematics contest problem, is summed up the summation to the multivariate square of integer variable and fuctional minimum. The sum of variable equals to a integer constant. The problem of such fuctional minimum and maximum is the most important Mathematics one. About the problem's summation, the article establishes complete theory, and gives a general way to solve.
