因子链上的最大公因数幂矩阵与最小公倍数幂矩阵

Divisibility of Determinants of Power Matrices on Divisor Chains

设S={x1,…,xn}是由n个不同正整数组成的集合,ε∈Z+.本文研究了对ε∈Z+定义在任意因子链S上的幂矩阵(S)εn间的整除性.n与det[S]εn和[S]εn的奇异性及它们的行列式det(S)

Let S={x_1,…,x_n} be a set of n distinct positive integers,ε∈Z^+.In this paper,I have researched that when ε∈Z^+,singularity of the power matrix (S)~ε_n and the [S]~ε_n defined on any divisor chain S and divisibility of the det(S)~ε_n and the det[S]~ε_n.