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On 3-Regular Tripartitions

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Abstract

In this article, we investigate the arithmetic behavior of the function D3(n) which counts the number of 3-regular tripartitions of n. For example, we show that for α ≥ 1 and n ≥ 0,

$${D_3}\left( {{3^{2\alpha }}n + \frac{{11 \cdot {3^{2\alpha - 1}} - 1}}{4}} \right) \equiv 0\left( {\bmod {3^{2\alpha + 3}}} \right)$$

and

$${D_3}\left( {{3^{2\alpha }}n + \frac{{7 \cdot {3^{2\alpha - 1}} - 1}}{4}} \right) \equiv 0\left( {\bmod {3^{2\alpha + 2}}} \right)$$

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Acknowledgements

The authors thank the referee for his/her many valuable suggestions which enhanced the quality of presentation of this paper.

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Authors and Affiliations

  1. Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru, 570006, Karnataka, India

    Chandrashekar Adiga & Ranganatha Dasappa

  2. Department of Mathematics, School of Physical Sciences, Central University of Karnataka, Kalaburagi, 4585367, Karnataka, India

    Ranganatha Dasappa

Authors
  1. Chandrashekar Adiga
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  2. Ranganatha Dasappa
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Correspondence to Ranganatha Dasappa.

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Adiga, C., Dasappa, R. On 3-Regular Tripartitions. Acta. Math. Sin.-English Ser. 35, 355–368 (2019). https://doi.org/10.1007/s10114-018-7111-0

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  • DOI: https://doi.org/10.1007/s10114-018-7111-0

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