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Mixed sums of squares and triangular numbers  HuiQin Cao
; Song Guo
; Hao Pan
; ZhiWei Sun
;  Date: 
10 May 2005  Subject:  Number Theory; Combinatorics MSCclass: 11E25; 11D85; 11P99  math.NT math.CO  Abstract:  For 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  Services:  Forum  Review  PDF  Favorites 


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