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

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