A General relation between sums of squares and sums of triangular numbers

Adiga, Chandrashekar and Cooper, Shaun and Han, Jung Hun (2005) A General relation between sums of squares and sums of triangular numbers. International Journal of Number Theory, 01 (02). pp. 175-182. ISSN 1793-7310

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Official URL: https://doi.org/10.1142/S1793042105000078

Abstract

Let rk(n) and tk(n) denote the number of representations of n as a sum of k squares, and as a sum of k triangular numbers, respectively. We give a generalization of the result rk(8n + k) = cktk(n), which holds for 1 ≤ k ≤ 7, where ck is a constant that depends only on k. Two proofs are provided. One involves generating functions and the other is combinatorial.

Item Type: Article
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: manjula User
Date Deposited: 05 Sep 2019 10:31
Last Modified: 05 Sep 2019 10:31
URI: http://eprints.uni-mysore.ac.in/id/eprint/7658

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