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In algebra, a Pythagorean field is a field in which every sum of two squares is a square: equivalently it has Pythagoras number equal to 1. A Pythagorean extension of a field F {\displaystyle F} is an extension obtained by adjoining an element 1 + λ 2 {\displaystyle {\sqrt {1+\lambda ^{2}}}} for some λ {\displaystyle \lambda } in F {\displaystyle F}. So a Pythagorean field is one closed under taking Pythagorean extensions. For any field F {\displaystyle F} there is a minimal Pythagorean field F p y {\textstyle F^{\mathrm {py} }} containing it, unique up to isomorphism, called its Pythagorean closure. The Hilbert field is the minimal ordered Pythagorean field.