模n王后和有关组合问题的研究

MODULAR QUEEN PROBLEM AND RELATED COMBINATORIAL PROBLEM

本文总结了关于模 n—王后问题和有关组合问题的已有结论,证明了当 gcd(n,12)=6时,M(n)=n-2,且证明了下列四个命题是等价的:①m(n)=n;②存在幻和为1的 n 阶全幻方;③存在 n 阶全对角线拉丁方;④存在正交 n 阶全角线拉丁方。

In this paper,we summarige much of the work done on modular queen problem and related Combi- uatorial problems,that following four propositions are eguivaleut: i)M(n)=n. ii)There exists a pandiagonal magic Square of orde n with magic sum 1. iii)There exists a pandiagonal Latin Square of order n Ⅳ)There exists a pair of orthogonal Pandiagonal Latin Square of order n.