Mixed sums of squares and triangular numbers (II)

Details Mixed sums of squares and triangular numbers (II) Mixed sums of squares and triangular numbers (II)

2005-05-10

arxiv.org/abs/math/0505187v5

Integers 7(2007), A56, 5 pp

Mathematics

Number Theory

Scientific paper

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.

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