Waste less time on Facebook — follow Brilliant.
×

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, 2 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} \( \boxed{123} \)

Comments

Sort by:

Top Newest

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, 2 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...