Parity results for 9-regular partitions |
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Authors: | Ernest X. W. Xia Olivia X. M. Yao |
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Affiliation: | 1. Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R. China
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Abstract: | Let t≥2 be an integer. We say that a partition is t-regular if none of its parts is divisible by t, and denote the number of t-regular partitions of n by b t (n). In this paper, we establish several infinite families of congruences modulo 2 for b 9(n). For example, we find that for all integers n≥0 and k≥0, $$b_9 biggl(2^{6k+7}n+ frac{2^{6k+6}-1}{3} biggr)equiv 0 quad (mathrm{mod} 2 ). $$ |
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