Abstract
Magic rectangles are a generalization of magic squares that have been recently investigated by Bier and Rogers (European J. Combin. 14 (1993) 285–299); and Bier and Kleinschmidt (Discrete Math. 176 (1997) 29–42). In this paper, we present a new, simplified proof of the necessary and sufficient conditions for a magic rectangle to exist. We also show that magic rectangles, under the natural multiplication, have a unique factorization as a product of irreducible magic rectangles.
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