The four squares-square theorem from the Gauss-Legendre three squares-square theorem

Hi, I'veI've been studying some proofs of Thethe four squares-square theorem. Some of them are pretty clear. However, I came across a statement that Thethe four squares-square theorem can be easily derived from Gauss-Legendre three squares-square theorem. Hard as I tried, I couldn't find out how to do it.

I was hoppinghoping someone could give me some idea or point out some article.

Thank you!

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edited Mar 16, 2013 at 16:40

Andrés E. Caicedo

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asked Mar 16, 2013 at 10:24

user32252

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The four squares theorem from the Gauss-Legendre three squares theorem

Hi, I've been studying some proofs of The four squares theorem. Some of them are pretty clear. However, I came across a statement that The four squares theorem can be easily derived from Gauss-Legendre three squares theorem. Hard as I tried, I couldn't find out how to do it.

I was hopping someone could give me some idea or point out some article.

Thank you!

nt.number-theory proof-theory sums-of-squares

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The four squares-square theorem from the Gauss-Legendre three squares-square theorem

The four squares theorem from the Gauss-Legendre three squares theorem

The four-square theorem from the Gauss-Legendre three-square theorem

The four squares theorem from the Gauss-Legendre three squares theorem