If ''n'' is a prime number, then the set of non-zero indices ''k'' = 1,...,''n''–1 forms a [[group (mathematics)|group]] under multiplication [[modulo]] ''n''. One consequence of thisthe [[number theory]] of such groups is that there exists a [[generating set of a group|generator]] of the group, an integer ''g'' such that ''k'' = ''g''<sup>''q''</sup> (mod ''n'') for any non-zero index ''k'' and for a unique ''q'' in 0,...,''n''–2 (forming a [[bijection]] from ''q'' to non-zero ''k''). Similarly ''j'' = ''g''<sup>–''p''</sup> (mod ''n'') for any non-zero index ''j'' and for a unique ''p'' in 0,...,''n''–2, where the negative exponent denotes the multiplicative inverse of ''g''<sup>''p''</sup> modulo ''n''. That means that we can rewrite the DFT using these new indices ''p'' and ''q'' as:
