  
  
Stat 
Members: 2831 Articles: 1'983'807 Articles rated: 2574
11 August 2020 

   

Article overview
 

Each natural number is of the form x^2+(2y)^2+z(z+1)/2  ZhiWei Sun
;  Date: 
9 May 2005  Subject:  Number Theory; Combinatorics MSCclass: 11E25; 05A30; 11B65; 11D85; 11P99  math.NT math.CO  Abstract:  In this paper we investigate mixed sums of squares and triangular numbers. By means of qseries, we prove that any natural number n can be written as x^2+(2y)^2+T_z with x,y,z in Z and T_z=z(z+1)/2, this is stronger than a conjecture of Chen. Also, we can express n in any of the following forms: x^2+2y^2+T_z, x^2+2y^2+2T_z, x^2+2y^2+4T_z, x^2+4y^2+2T_z, 2x^2+2y^2+T_z, x^2+2T_y+2T_z, x^2+4T_y+T_z, x^2+4T_y+2T_z, 2x^2+T_y+T_z, 2x^2+2T_y+T_z, 2x^2+4T_y+T_z, T_x+4T_y+T_z, 2T_x+2T_y+T_z, 2T_x+4T_y+T_z. Concerning the converse we establish several theorems and make some conjectures.  Source:  arXiv, math.NT/0505128  Services:  Forum  Review  PDF  Favorites 


No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser CCBot/2.0 (https://commoncrawl.org/faq/)

 



 News, job offers and information for researchers and scientists:
 