Abstract
Let Tℓ(n) denote the number of ℓ-regular partition triples of n. In this paper, we consider the arithmetic properties of T7(n). An infinite family of congruences modulo powers of 7 and several congruences modulo 7 are established. For instance, we prove that for all n ≥ 0 and α ≥ 1,
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Acknowledgement
The authors would like to thank the referee for his/her careful reading and helpful comments on an earlier version of this paper. The second author was supported by the National Natural Science Foundation of China (No. 11501061) and the Fundamental Research Funds for the Central Universities (No. 2018CDXYST0024). The third author was supported by the National Natural Science Foundation of China (No. 11571143) and Jiangsu National Funds for Distinguished Young Scientists (No. BK20180044).
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Chern, S., Tang, D. & Xia, E.X.W. Arithmetic properties for 7-regular partition triples. Indian J Pure Appl Math 51, 717–733 (2020). https://doi.org/10.1007/s13226-020-0426-4
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DOI: https://doi.org/10.1007/s13226-020-0426-4