Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/19756
Title: 
Authors: 
Issue Date: 
2013
Citation: 
Toh, P. C. (2013). On representations by figurate numbers: A uniform approach to the conjectures of Melham. International Journal of Number Theory, 9(4), 1055-1071. https://doi.org/10.1142/S1793042113500127
Abstract: 
Using known formulas for R(a;b)(n), the number of representations of n as a times a square plus b times a square, we prove 21 conjectured formulas of Melham on the number of representations of n as sums of triangular, pentagonal and heptagonal numbers. We also demonstrate how our technique can be used to prove the other 277 conjectured formulas of Melham concerning representations by other gurate numbers.
Description: 
This is the final draft, after peer-review, of a manuscript published in International Journal of Number Theory. The published version is available online at https://doi.org/10.1142/S1793042113500127
URI: 
ISSN: 
1793-0421 (print)
1793-7310 (online)
Other Identifiers: 
10.1142/S1793042113500127
Appears in Collections:Journal Articles

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