AN INFINITE FAMILY OF OVERPARTITION CONGRUENCES MODULO 12
AN INFINITE FAMILY OF OVERPARTITION CONGRUENCES MODULO 12
复制标题
作者：
M. Hirschhorn;James A. Sellers
最近证明了过划分的一些算术性质。然而，所有这些结果都涉及模是2的幂。在这个简短的注记中，我们通过证明对所有n≥0和所有α≥0，p(9α(27n+18))≡0(Mod 12)，证明了第一个模不是2的幂的同余无限族。
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).