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 ${\displaystyle p(K)}$ of a field ${\displaystyle p}$ is the smallest positive integer ${\displaystyle p}$ such that every sum of squares in ${\displaystyle K}$ is a sum of ${\displaystyle p}$ squares.

A Pythagorean field is a field with Pythagoras number 1: that is, every sum of squares is already a square.