Mixed Sums of Squares and Triangular Numbers

نویسندگان

  • Hui-Qin Cao
  • Song Guo
  • Hao Pan
  • Zhi-Wei Sun
  • SONG GUO
  • HAO PAN
  • ZHI-WEI SUN
چکیده

For x ∈ Z let Tx 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 ∈ Z: x + Ty + Tz , x 2 + 2Ty + Tz , x 2 + 3Ty + Tz , x + 5Ty + 2Tz , x 2 + 6Ty + Tz , 3x 2 + 2Ty + Tz , x + 3y + Tz , 2Tx + Ty + Tz , 3Tx + 2Ty + Tz , 5Tx + Ty + Tz . This confirms some conjectures raised by Sun.

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تاریخ انتشار 2005