An essential part of the resolution method widely used in artificial intelligence (e.g., in Prolog) is unification of terms t_i, i.e., finding a substitution s for which s(t₁) = S(t_{- 2}). The paper under review is devoted to the unification problem for terms built from variables x_i and constants c_i by means of an associative and commutative function symbol +. In general, this problem is NP-complete. The author proposes the following approach to this problem. The set of all terms can be embedded into the linear space over Q with base, consisting of x_i and c_i. In terms of this linear space substitution, s is a linear operation, corresponding to a special type matrix with integral coefficients. This fact reduces the unification problem to the problem of finding integer solutions of linear equations. This reduction leads to a fast parallel algorithm for the case when each of the terms contains variables.