Arabian Journal of Mathematics

, Volume 7, Issue 2, pp 61–75 | Cite as

Congruences modulo 8 for \((2,\, k)\)-regular overpartitions for odd \(k > 1\)

  • Chandrashekar Adiga
  • M. S. Mahadeva Naika
  • D. Ranganatha
  • C. Shivashankar
Open Access


In this paper, we study various arithmetic properties of the function \(\overline{p}_{2,\,\, k}(n)\), which denotes the number of \((2,\,\, k)\)-regular overpartitions of n with odd \(k > 1\). We prove several infinite families of congruences modulo 8 for \(\overline{p}_{2,\,\, k}(n)\). For example, we find that for all non-negative integers \(\beta , n\) and \(k\equiv 1\pmod {8}\), \(\overline{p}_{2,\,\, k}(2^{1+\beta }(16n+14))\equiv ~0\pmod {8}\).

Mathematics Subject Classification

05A15 05A17 11P83 



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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Studies in MathematicsUniversity of MysoreMysoreIndia
  2. 2.Department of MathematicsBangalore UniversityBangaloreIndia
  3. 3.Department of MathematicsSiddaganga Institute of TechnologyTumakuruIndia

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