正交泛对角线拉丁方与泛对角线幻方(Ⅱ)

ORTHOGONAL PANDIAGONAL LATIN SQUARES AND PANDIAGONAL MAGIC SQUARE(Ⅱ)

本文给出数集构成对角线幻方的必要条件,证明由数集M={1,2,…,(4t+2)~2}(t≥0)不能构成4t+2阶泛对角线幻方,并证明2t(t≥1)阶泛对角线拉丁方不存在。

This paper gives necessary condition constructing pandiagonal magic square for number set and proves that pandiagnal magic squareof order 4t+2 (t>0) can not be constructed from number set M={1,2,...,(4t+2)~2}, further, it is proved that there exists no pandiagonal Latin square of order 2t for every positive integer t t>1.