在商环z／（n）（n＞2奇数）上构造奇数阶正交拉丁方

Construction of Orthogonal Latin Squares with Odd Order on Quotient Ring Z/(n)

设ｎ为大于２的奇数。本文在商环ｚ／（ｎ）上证明了：至少存在Ｋ个两两正文的ｎ阶拉丁方。这里ｋ满足（ｎ＿ｌ，ｎ）＝１．ｎ＿ｌ＜ｎ，且ｌ≠ｍ，ｎ＿ｌ＞ｎ＿ｍ时，（ｎ＿ｌ－ｎ＿ｍ，ｎ）＝１，ｌ，ｍ＝１，２，．．．，ｋ．

Let n > 2 be an odd number,k,n_l,n_m be integers such that(n_l,n)=1 for n_l < nand(n_l -n_m,n)=1 for l≠m, n_l>n_m,l,m=1,2,...,k. This paper proves that there existat least k orthogonal Latin squares with n order.