A general relation between sums of cubes and triangular pyramidal numbers
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...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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American Institute of Physics
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57336/ http://psasir.upm.edu.my/id/eprint/57336/1/A%20general%20relation%20between%20sums%20of%20cubes%20and%20triangular%20pyramidal%20numbers.pdf |
| _version_ | 1848853336625774592 |
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| author | Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana |
| author_facet | Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana |
| author_sort | Mohamat Johari, Mohamat Aidil |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T10:52:21Z |
| format | Conference or Workshop Item |
| id | upm-57336 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:21Z |
| publishDate | 2011 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-573362017-09-26T04:07:05Z http://psasir.upm.edu.my/id/eprint/57336/ A general relation between sums of cubes and triangular pyramidal numbers Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana 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. American Institute of Physics 2011 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57336/1/A%20general%20relation%20between%20sums%20of%20cubes%20and%20triangular%20pyramidal%20numbers.pdf 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). 10.1063/1.4724154 |
| spellingShingle | Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana A general relation between sums of cubes and triangular pyramidal numbers |
| title | A general relation between sums of cubes and triangular pyramidal numbers |
| title_full | A general relation between sums of cubes and triangular pyramidal numbers |
| title_fullStr | A general relation between sums of cubes and triangular pyramidal numbers |
| title_full_unstemmed | A general relation between sums of cubes and triangular pyramidal numbers |
| title_short | A general relation between sums of cubes and triangular pyramidal numbers |
| title_sort | general relation between sums of cubes and triangular pyramidal numbers |
| url | http://psasir.upm.edu.my/id/eprint/57336/ http://psasir.upm.edu.my/id/eprint/57336/ http://psasir.upm.edu.my/id/eprint/57336/1/A%20general%20relation%20between%20sums%20of%20cubes%20and%20triangular%20pyramidal%20numbers.pdf |