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AN INFINITE FAMILY OF OVERPARTITION CONGRUENCES MODULO 12

A number of arithmetic properties of overpartitions have been proven recently. However, all such results have involved moduli which are powers of 2. In this brief note, we prove the first infinite family of congruences with a modulus that is not a power of 2 by proving that, for all n ≥ 0 and all α ≥ 0, p(9 α (27n + 18)) ≡ 0 (mod 12).