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Gauss proved that every integer is expressible as the sum of three triangular numbers. I was wondering if the proof is anywhere to be found?

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  • $\begingroup$ there is a proof here, but it relies on the 3 square theorem $\endgroup$ – Alessandro Codenotti Sep 20 '15 at 13:51
  • $\begingroup$ Gauss proved it without using the three square theorem. $\endgroup$ – wowlolbrommer Sep 20 '15 at 13:53
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    $\begingroup$ are you sure about that? My latin is very bad, but on art 293 (page 515 of the pdf) Gauss proves the results you're interested in and it seems to use the fact that every integer of the form $8M+3$ can be written as the sum of 3 squares. Anyway, whether the proof uses the 3 squares theorem or not it was published by Gauss in the book I linked, I'm not sure whether you need someone who can read Latin or whether there is an English version $\endgroup$ – Alessandro Codenotti Sep 20 '15 at 14:13

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