The author proves the following theorem: Given a locally finite semisimple arithmetical variety. For each natural number n there exists a term \(t_ n(x,y,z,u_ 1,...,u_ n)\) such that in any n-generated simple algebra, with generators \(s_ 1,...,s_ n\) the polynomial \(t_ n(x,y,z,s_ 1,...,s_ n)\) is a discriminator polynomial.
A corollary of this is the result of A. Pixley saying that an arithmetical variety generated by a finite set K of finite simple algebras is a discriminator variety if and only if the members of K are hereditarily simple.