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In this short article, two recent beautiful proofs of George Andrews, AviezriFraenkel, and James Sellers, about the mod m characterization of the number ofm-ary partitions are simplified and streamlined, and then generalized to handlemany more cases, and prove much deeper theorems, with the help of computers, ofcourse.

Computerizing the Andrews-Fraenkel-Sellers Proofs on the Number of m-ary partitions mod m (and doing MUCH more!)