The Reversion of Class Number Relations and the Total Representation of Integers as Sums of Squares or Triangular Numbers

1921 ◽  
Vol 23 (1) ◽  
pp. 56
Author(s):  
E. T. Bell
Keyword(s):  
Class Number ◽  
Sums Of Squares ◽  
Triangular Numbers ◽  
Representation Of Integers

On the representation of integers as sums of triangular numbers

1995 ◽  
Vol 50 (1-2) ◽  
pp. 73-94 ◽  
Author(s):  
Ken Ono ◽  
Sinai Robins ◽  
Patrick T. Wahl
Keyword(s):  
Triangular Numbers ◽  
Representation Of Integers

Proofs of Some Conjectures of Z. -H. Sun on Relations Between Sums of Squares and Sums of Triangular Numbers

2020 ◽  
Vol 51 (1) ◽  
pp. 11-38
Author(s):  
Nayandeep Deka Baruah ◽  
Mandeep Kaur ◽  
Mingyu Kim ◽  
Byeong-Kweon Oh
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

Triangular Numbers and Sums of Squares

1988 ◽  
Vol 72 (462) ◽  
pp. 297
Author(s):  
C. J. Bradley
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

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

2005 ◽  
Vol 01 (02) ◽  
pp. 175-182 ◽  
Author(s):  
CHANDRASHEKAR ADIGA ◽  
SHAUN COOPER ◽  
JUNG HUN HAN
Keyword(s):  
Generating Functions ◽  
General Relation ◽  
The Other ◽  
Sums Of Squares ◽  
Triangular Numbers

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.

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