一个数论问题——自然数圈的等和三段的划分

A NUMBER THEORY PROBLEM-PARTITION OF NATURAL NUMBER CIRCLE IN THREE SECTIONS OF EQUAL SUM

本文提出一个数论问题,要求求出所有的正整数 n(>3) ,使得自然数圈1,2,3,…,n-1,n 能被划分成三段,每段上的各数之和相等.本文证明了这样的 n 有无穷多个,并用递推公式给出了无穷多个这样的 n.

In this paper,we propose a number theory problem as follows:Determine all positive interger n(>3) such that the natural number circle 1,2,…,n-1,n can be partitioned in three sections of equal sum.We prove that the number of these n is infinite and give a recurrence formula ofn in partly.