On equality of some elements in matrices

AbstractIf the non-zero entries of a matrix S satisfy certain sum restrictions, then it is shown that all these entries must be equal. This paper is prompted by a conjecture of Wang [2]. Not only is the conjecture proved, but the basic underlying idea is abstracted and the result extended considerably. The techniques given here have been successfully employed by the author in obtaining significant results on (0,1) matrices and Latin squares (to appear elsewhere)