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.

Not to be confused with Pythagoras's constant or height of a field.

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

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