A complete solution to the existence of normal bimagic squares of even order

Abstract

Magic square is an ancient and important subject in combinatorial mathematics, and many kinds of magic square are studied and concerned by many scholars, in particular, the existence of normal bimagic squares has been studied for over one hundred years. In this paper, the existence of the normal bimagic squares of even order is investigated, the ideas of general row (column) bimagic rectangles and magic pairs are introduced, which are applied to our construction, then we obtain the spectrum of the normal bimagic squares of even order, in other words, it is shown that there exists a normal bimagic square of order 2u if and only if u≥4.