Construction of magic rectangles of odd order

Magic rectangles are well-known for their very interesting and entertaining combinatorics. Such magic rectangles have also been used in designing experiments. In a magic rectangle, the integers 1 to pq are arranged in an array of p rows and q columns so that each row adds to the same total P and each column to the same total Q. In the present paper we provide a systematic method for constructing a p by q magic rectangle where p > 1 and q > 1 are any odd integers.