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1. Introduction. An underlying goal of the research reported here is to develop a theory showing that the process of multiplying decimal integers is intrinsically more difficult than the process of adding them (2). In part I of this paper we present a precise conjecture which is a possible formulation of this proposition. The formulation is not completely satisfactory, but it certainly bears on the problem and raises interesting mathematical questions. Part II contains a proof of a weakened form of the conjecture.

There are several different ways in which multiplication seems to be more difficult than addition, and each could lead to a different formulation of the problem. For example, experience of computer designers indicates that it takes more circuitry to compute the fixed-point product of two n-digit integers than to find the sum. Again, even with the increased circuitry, the time required to carry out the multiplication exceeds that …