대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권3호
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  • Pages.477-482
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  • 2012
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON PARTITION CONGRUENCES FOR OVERCUBIC PARTITION PAIRS

  • Kim, Byung-Chan (School of Liberal Arts Seoul National University of Science and Technology)
  • 투고 : 2011.04.26
  • 발행 : 2012.07.31
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초록

In this note, we investigate partition congruences for a certain type of partition function, which is named as the overcubic partition pairs in light of the literature. Let $\bar{cp}(n)$ be the number of overcubic partition pairs. Then we will prove the following congruences: $$\bar{cp}(8n+7){\equiv}0(mod\;64)\;and\;\bar{cp}(9m+3){\equiv}0(mod\;3)$$.

키워드

참고문헌

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  2. B. C. Berndt, Number Theory in the Spirit of Ramanujan, American Mathematical Society, Providence, RI, 2006.
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피인용 문헌

  1. Congruences modulo 27 for cubic partition pairs vol.171, 2017, https://doi.org/10.1016/j.jnt.2016.07.012
  2. New congruences for overcubic partition pairs vol.10, pp.4, 2017, https://doi.org/10.1515/tmj-2017-0050