柯召、孙琦—单墫定理的拓广

The Generalized Ke Zhao, Sun Qi and Shan Zhen Theorem

一、引言人们容易证明任意3个整数中必有两个整数之和为2整除,任意5个整数中必有3个整数之和为3整除,柯老和孙琦教授在[1]中证明了任意7个整数中必有4个整数之和为4整除,并猜测任意2n-1(n>1)个整数中必有n个整数之和能为n整除。

Ke Zhao and Sun Qi ever conjectured that for any 2n-1 (n>1) integers inwhich there exist certainly n integers whose sum is divided by n. The conjecture provedby Shan Zhen in 1982. In this paper, we have generalized this conjecture to the scope ofalgebraic integers contained in any one algebraic number field.