SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS INDUCED BY PARTITIONS OF 8-Reference-Cited by-同舟云学术

SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS INDUCED BY PARTITIONS OF 8

Published:2008-08 Issue:04 Volume:04 Page:525-538
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BARUAH NAYANDEEP DEKA¹,COOPER SHAUN²,HIRSCHHORN MICHAEL³

Affiliation:

1. Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India

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

3. School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia

Abstract

Let rk(n) and tk(n) denote the number of representations of an integer n as a sum of k squares, and as a sum of k triangular numbers, respectively. We prove that [Formula: see text] and therefore the study of the sequence t8(n) is reduced to the study of subsequences of r8(n). We give an additional 21 analogous results for sums of squares and sums of triangular numbers induced by partitions of 8. We give a brief indication of what happens for the case k ≥ 9.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304210800150X

Reference8 articles.

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

2. Relations between squares and triangles

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

4. Ramanujan’s Notebooks

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