Mixed sums of squares and triangular numbers (II)

Song Guo; Hao Pan; Zhi-Wei Sun

Mixed sums of squares and triangular numbers (II)

Number Theory 2007-12-24 v5 Combinatorics

Authors: Song Guo , Hao Pan , Zhi-Wei Sun

Abstract

For an integer $x$ let $t_x$ denote the triangular number $x(x+1)/2$ . Following a recent work of Z. W. Sun, we show that every natural number can be written in any of the following forms with $x,y,z\in\Z$ : $x^2+3y^2+t_z, x^2+3t_y+t_z, x^2+6t_y+t_z, 3x^2+2t_y+t_z, 4x^2+2t_y+t_z.$ This confirms a conjecture of Sun.

Keywords

number theory perfect numbers

Cite

@article{arxiv.math/0505187,
  title  = {Mixed sums of squares and triangular numbers (II)},
  author = {Song Guo and Hao Pan and Zhi-Wei Sun},
  journal= {arXiv preprint arXiv:math/0505187},
  year   = {2007}
}

Mixed sums of squares and triangular numbers (II)

Abstract

Keywords

Cite

Related papers