Timeline for 3 square theorem

10 events

when toggle format	what		by	license	comment
Jul 16, 2021 at 17:13	history	edited	YCor		edited tags
Jan 5, 2011 at 18:04	vote	accept	t.k
Jan 5, 2011 at 18:04	vote	accept	t.k
Jan 5, 2011 at 18:04
Dec 31, 2010 at 10:22	history	edited	Pete L. Clark	CC BY-SA 2.5	deleted 3 characters in body
Dec 30, 2010 at 3:29	answer	added	Will Jagy		timeline score: 7
Dec 29, 2010 at 10:44	comment	added	Qiaochu Yuan		Do you know a proof which doesn't? (Not rhetorical; I only know one proof.)
Dec 29, 2010 at 9:54	answer	added	Pete L. Clark		timeline score: 6
Dec 29, 2010 at 8:22	comment	added	Alex B.		Google does. Here is a concrete application towards the 3-square theorem: to prove that $M\equiv 3\pmod{8}$ is a sum of three integer squares, apply the Hasse principle to the form $x^2 + y^2 + z^2 - Mw^2$ and thereby show that this form represents 0 over $\mathbb{Q}$ (it does so over all completions). Using Cassels's (sic) lemma completes the proof of the theorem for $M\equiv 3\pmod{8}$.
Dec 29, 2010 at 8:13	comment	added	Kevin Buzzard		Assuming you mean the standard classification of which integers are the sum of three integer squares, the only other thing you need is the local-global principle, which is true in this situation (Hasse-Minkowski). See for example Serre's book "A course in arithmetic". The reason you get the funny $4^m(8n+7)$ business is the local condition at 2; all other local conditions are satisfied.
Dec 29, 2010 at 8:04	history	asked	t.k	CC BY-SA 2.5