关于立方数集合二分拆

On the Two Partitions of Cubic Set

研究立方数集合M的二分拆问题T2(n):能否将集合M={13,23,…,n3}分成二个互不相交的子集A1、A2的并集,并且每个子集Ai的元素之和相等。研究结果获得了问题T2(n)有解的充要条件是n≡0,3(mod 4)且n≠3,4,7,8,11。最后,提出了关于循环周期的一些猜想。

This paper studies the two partitions of cubic set M = { 1^3,2^3,..., n^3 } for problem T2 （n） , and discusses whether the set M can be decomposed into the union set of two mutually disjoint subset A1 ,A2,…… ,Ak and the sum of each subset Ai （1 〈 i 〈 k） is equal to each other. Then it obtains the result that the important necessary and sufficient condition for the solved problem T2 （n） is n ≡0,3 （mod4） , but n ≠ 3,4,7,8,11. Finally, some con- jectures about circulatory cycle are proposed