Yang Hui Type Magic Squares with \(t\)-Powered Sum

Abstract

In this paper, the existence of Yang Hui type magic squares of order \(n\) with \(t\)-powered sum (YMS(\(n\), \(t\))) for general \(t\) is investigated. Some constructions of YMS(\(n\), \(t\)) are obtained by using strongly symmetric self-orthogonal diagonal Latin squares and magic rectangles. Applying these constructions, it is proved that for an integer \(t > 1\) there exist both a symmetric elementary YMS(\(2^t\), \(2t – 2\)) and a symmetric elementary YMS(\(2^t – k\), \(2t\)) for odd \(k > 1\), which improves the known result on YMSs.