N-digit, radix-a bases are proposed for VLSI implementation of redundant arithmetic, mod m, where a N m = ±1, a j m π ±1, for 0 < j < N and m is prime. These bases simplify arithmetic overflow and are well suited to redundant arithmetic. The representations provide competitive, multiplierless T-point Number Theoretic Transforms, mod m, where T | N or T | 2N. Index Terms-Modular arithmetic, redundant number systems, number theoretic transforms, residue and polynomial number systems.