Abstract
We give a complete characterisation of the parity of \(b_8(n)\), the number of 8-regular partitions of n. Namely, we prove that \(b_8(n)\) is odd precisely when \(24n+7\) has the form \(p^{4a+1}m^2\) with p prime and \(p\not \mid m\).
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Acknowledgements
G.C. is a Researcher at INdAM. He also received support by Czech Science Foundation GACR, Grant 21-00420M, Project PRIMUS/20/SCI/002 from Charles University, and Charles University Research Centre Program UNCE/SCI/022. This work began during a visit of P.M. to Charles University, which we thank for the support and the hospitality. We thank the referees for their useful suggestions which helped us improve the exposition.
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G.C. received support by Czech Science Foundation GACR, Grant 21-00420M, Project PRIMUS/20/SCI/002 from Charles University, and Charles University Research Centre Program UNCE/SCI/022.
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Cherubini, G., Mercuri, P. Parity of the 8-regular partition function. Ramanujan J 63, 715–722 (2024). https://doi.org/10.1007/s11139-023-00784-4
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DOI: https://doi.org/10.1007/s11139-023-00784-4