Mixed sums of squares and triangular numbers (II)

Original · EN

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.