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13 July 2020
 
  » arxiv » math.NT/0505187

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Mixed sums of squares and triangular numbers
Hui-Qin Cao ; Song Guo ; Hao Pan ; Zhi-Wei Sun ;
Date 10 May 2005
Subject Number Theory; Combinatorics MSC-class: 11E25; 11D85; 11P99 | math.NT math.CO
AbstractFor an integer x let T_x denote the triangular number x(x+1)/2. Following the recent approach of Z. W. Sun, we show that every natural number can be written in any of the following forms with x,y,z in Z: 4x^2+T_y+T_z, 4x^2+2T_y+T_z, x^2+3T_y+T_z, x^2+5T_y+2T_z, x^2+6T_y+T_z, 3x^2+2T_y+T_z, x^2+3y^2+T_z, 2T_x+T_y+T_z, 3T_x+2T_y+T_z, 5T_x+T_y+T_z.
Source arXiv, math.NT/0505187
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