Mixed sums of squares and triangular numbers (II)
Song Guo, Hao Pan, Zhi-Wei Sun
Abstract
For an integer x let tx 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∈: x2+3y2+tz, x2+3ty+tz, x2+6ty+tz, 3x2+2ty+tz, 4x2+2ty+tz. This confirms a conjecture of Sun.
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