A new proof of the theorem on exponential diophantine representation of enumerable sets

A new proof is given for the well-known theorem of Putnam, Davis, and Robinson on exponential diophantine representation of recursively enumerable sets. Starting from the usual definition of r.e. sets via Turing machines, a new method of arithmetization is given. This new method leads directly to a purely existential exponential formula. The new proof may be more suitable for a course on the theory of algorithms because it requires less knowledge of number theory.