Publications

Abstract : A quasimagic rectangle Q M R ( a , b : d ) is an a ? b array with a odd and b even whose entries are 1 , 2 , ? , d ? 1 , d + 1 , ? , a b + 1, each appearing exactly once, such that the sum of every row is equal to a constant ? and the sum of every column is equal to a constant σ. In this article, we prove the existence of Q M R ( a , b : d ) for all possible values of a and b, when d = a b ? 2 + 1. In addition, if g c d ( a , b ) = 1, we prove that the condition d = a b ? 2 + 1 is necessary and sufficient for the existence of Q M R ( a , b : d ).