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.

#NumberTheory

Easy Math Editor

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Comments

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 - 4 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$