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I am planning to write a little note detailing several proofs of Lagrange's theorem that every natural number can be written as the sum of four perfect squares. I know of three different proofs so far:

  • a completely elementary proof by descent.
  • a proof via Minkowski's theorem and lattices.
  • Jacobi's proof via modular forms.

Can anybody think of any more nice, relatively elementary proofs of this result? Thanks in advance.

  • 0
    I remember hearing of a probabilistic result from Erdos related to Lagrange's theorem, perhaps it has an actual proof.2010-12-31
  • 0
    Is there something I am missing here? 1 is a natural number, but it can not be written as a sum of four squares?2011-12-10
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    @N3buchadnezzar: $1=1^2+0^2+0^2+0^2$2014-02-08
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    would you pls share your note when it's available?2014-04-27

4 Answers 4