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Out of “Pillow Problems” (Posted on 2021-03-15)

Three times sum of three squares equals sum of four squares.

Prove it!

Attributed to Lewis Carroll.

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (2 votes)

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Solution (Spoiler)

| Comment 1 of 2

All numbers are the sum of 4 squares, but that is hard to prove.

However, it is easy to prove that

3(a^2 + b^2 + c^2) =

(a-b)^2 + (a-c)^2 + (b-c)^2 + (a+b+c)^2

Posted by Steve Herman on 2021-03-15 21:24:14

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