Abstract

A generalization of regular magic squares with magic sum µ is an sq-corner (or square corner) magic square. It is a magic square satisfying the condition that the sum of 4 entries, square symmetrically placed with respect to the center, equals^4µ. Using the n sq-corner magic squares of order n, a construction of sq-corner magic squares of order n + 2 is derived. Moreover, this construction provides some nonsingular classical sq-corner magic squares of all orders. In particular, a nonsingular regular magic square of any odd order can be constructed under this new method, as well.