A general relation between sums of cubes and triangular pyramidal numbers

• Main Authors: Mohamat Johari, Mohamat Aidil, Mohd Atan, Kamel Ariffin, Sapar, Siti Hasana
• Format: Conference or Workshop Item
• Language: English
• Published: American Institute of Physics 2011
• Online Access: http://psasir.upm.edu.my/id/eprint/57336/1/A%20general%20relation%20between%20sums%20of%20cubes%20and%20triangular%20pyramidal%20numbers.pdf; http://psasir.upm.edu.my/id/eprint/57336/
• Institution: Universiti Putra Malaysia

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.