Abstract
Let \(a_t(n)\) denote the number of t-core partitions of n. In recent years, a number of congruences for \(a_t(n)\) have been discovered for some small t. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\). Motivated by their work, we prove some new infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\) by utilizing Newman's identities.
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This work was supported the Natural Science Foundation of Jiangsu Province of China (no. BK20221383).
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Meng, Z., Yao, O.X.M. New infinite families of congruences for 5-core and 7-core partitions. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01424-z
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DOI: https://doi.org/10.1007/s10474-024-01424-z