Assume that n is an integer not prime Show that you can find

Assume that n is an integer, not prime. Show that you can find two distributions a and b on the nonnegative integers such that the convolution of a and b is the equiprobable distribution on the set 0, 1, 2, ..., n - 1. If n is prime this is not possible, but the proof is not so easy. (Assume that neither a nor b is concentrated at 0.)

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