A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS-Reference-Cited by-同舟云学术

A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS

Published:2005-06 Issue:02 Volume:01 Page:175-182
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

ADIGA CHANDRASHEKAR¹,COOPER SHAUN²,HAN JUNG HUN¹

Affiliation:

1. Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570006, India

2. Institute of Information and Mathematical Sciences, Massey University — Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042105000078

Reference9 articles.

1. Special Functions

2. Relations between squares and triangles

3. Sums of Squares and the Preservation of Modularity under Congruence Restrictions

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