We give a complete characterization 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 $p\nmid m$.
Parity of the 8-regular partition function / Cherubini, G.; Mercuri, P.. - In: RAMANUJAN JOURNAL. - ISSN 1382-4090. - (2023). [10.1007/s11139-023-00784-4]
Parity of the 8-regular partition function
Mercuri P.
2023
Abstract
We give a complete characterization 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 $p\nmid m$.File allegati a questo prodotto
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