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Help with the four-square theorem

Those who know the proof of Lagrange's four-square theorem (which states that every positive integer can be written as sum of 4 squares), can you explicitly show the proof to me in simple words step by step, cuz the internet doesn't explain too clearly. A thought-out proof would be perfect. thx.

Note by William Isoroku
1 year ago

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This is just off the top of my head, but this could be connected to Goldbach's Conjecture, which says that every number is the sum of 2 primes, and there's another proof somewhere (I think) that says every prime of the form 4n+1 is the sum of 2 squares. So, there you go. It's an idea, anyway, something different than going by way of Hurwitz quaternions.

Edit: You might want to check Sum of Squares Theorems This is pretty well written and clear. Michael Mendrin · 1 year ago

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