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In short: it IS true in two three cases:

  • for polynomial of degree 2
  • for polynomial of degree 4 in two variables
  • for polynomial in one variable.

The answer is here:

Hilbert, D. Ueber die Darstellung deniter Formen als Summe von Formenquadraten. Mathem. Annalen Bd 32, S. 342-350 (1888)
show/hide this revision's text 1

In short: it IS true in two cases:

  • for polynomial of degree 2
  • for polynomial in one variable.

The answer is here:

Hilbert, D. Ueber die Darstellung deniter Formen als Summe von Formenquadraten. Mathem. Annalen Bd 32, S. 342-350 (1888)