Generalized Fermat-Mersenne number theoretic transform

A generalization of the Fermat and Mersenne number transform is suggested. The transforms are defined over finite fields and rings. This paper establishes the conditions necessary for these numbers to be prime. The length of the transforms is a highly composite number. An algorithm for finding primitive roots of unity is also discussed. The proposed transforms are characterized by respectable combinations of transform length, dynamic range and computational efficiency and can be used for fast convolution of integer sequences.<
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