The Ramanujan Journal

, Volume 34, Issue 1, pp 109–117 | Cite as

Parity results for 9-regular partitions



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,
$$b_9 \biggl(2^{6k+7}n+ \frac{2^{6k+6}-1}{3} \biggr)\equiv 0 \quad (\mathrm{mod}\ 2 ). $$


Partition Regular partition Congruence 

Mathematics Subject Classification

11P83 05A17 



The authors would like to thank the anonymous referees for valuable suggestions, corrections, and comments that resulted in a great improvement of the original manuscript.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsJiangsu UniversityZhenjiangP.R. China

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