Abstract
In this note, we establish two identities of \((q;\,q)_\infty ^8\) by using Jacobi’s four-square theorem and two of Ramanujan’s identities. As an important consequence, we present one Ramanujan-style proof of the congruence \(p_{-3}(11n+7)\equiv 0\ (\mathrm{mod\ }11)\), where \(p_{-3}(n)\) denotes the number of 3-color partitions of n.
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This work was supported by the National Natural Science Foundation of China (No. 11401253).
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Lin, B.L.S. Ramanujan-style proof of \(p_{-3}(11n+7) \equiv 0\ (\mathrm{mod\ }11)\) . Ramanujan J 42, 223–231 (2017). https://doi.org/10.1007/s11139-015-9733-5
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DOI: https://doi.org/10.1007/s11139-015-9733-5