A general relation between sums of cubes and triangular pyramidal numbers

Citation

Mohamat Johari, Mohamat Aidil and Mohd Atan, Kamel Ariffin and Sapar, Siti Hasana (2011) A general relation between sums of cubes and triangular pyramidal numbers. In: 5th International Conference on Research and Education in Mathematics (ICREM5), 22-24 Oct. 2011, Bandung, Indonesia. (pp. 275-279).

Abstract

Let ck(m) denote the number of representations of integer m as a sum of k cubes and pk(m) denote the number of representations of integer m as a sum of k triangular pyramidal numbers. We give a relation pk(m) = coddk (ν) where ν = 48m – 24n+2ñ+k and coddk (ν) denotes the number of representations of integer ν as a sum of k odd cubes, for a single value of m. A general relation between number of representations between Σki=1 xsi and its associated polytopic numbers for any orders of s, is also given.

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Additional Metadata

Item Type:	Conference or Workshop Item (Paper)
Divisions:	Institute for Mathematical Research
DOI Number:	https://doi.org/10.1063/1.4724154
Publisher:	American Institute of Physics
Keywords:	Number of representations; Sum of cubes; Sum of triangular pyramidal numbers
Depositing User:	Nabilah Mustapa
Date Deposited:	26 Sep 2017 04:07
Last Modified:	26 Sep 2017 04:07
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1063/1.4724154
URI:	http://psasir.upm.edu.my/id/eprint/57336
Statistic Details:	View Download Statistic

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