Geodesic
A criterion for the uniformity of the distribution of the sum of independent random variables on a primary cyclic group
Diskretnaya Matematika, Tome 9 (1997) no. 1, pp. 95-102.

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We consider the distribution of the sum of independent random variables which take their values from a primary cyclic group and are uniformly distributed on sets of identical cardinality. 
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B. V. Ryazanov; G. P. Shankin. A criterion for the uniformity of the distribution of the sum of independent random variables on a primary cyclic group. Diskretnaya Matematika, Tome 9 (1997) no. 1, pp. 95-102. http://geodesic.mathdoc.fr/item/DM_1997_9_1_a7/