Pythagoras number

In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number "p"("K") of a field "K" is the smallest positive integer "p" such that every sum of squares in "K" is a sum of "p" squares.
A "Pythagorean field" is a field with Pythagoras number 1: that is, every sum of squares is already a square.