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# Lagrange’s four-square theorem

Lagrange’s four-square theorem states that every non-negative integer may be expressed as the sum of at most four squares. By the Euler four-square identity, it is enough to show that every prime is expressible by at most four squares. It was later proved that only the numbers of the form $4^{n}(8m+7)$ require four squares.

This shows that $g(2)=G(2)=4$, where $g$ and $G$ are the Waring functions.

Related:

WaringsProblem, EulerFourSquareIdentity

Type of Math Object:

Theorem

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Reference

## Mathematics Subject Classification

11P05*no label found*

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