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## 'Sums of Squares' printed from http://nrich.maths.org/

This is a problem by Lewis Carroll and it revolves around some
of the many interesting properties of sums of squares of integers.
Is it always true that if you double the sum of two squares you get
the sum of two squares? If so can you prove it? Here are some
examples.

$2(5^2 + 3^2) = 2(25 + 9) = 68 = 64 + 4 = 8^2 + 2^2$

$2(7^2 + 4^2) = 2(49 + 16) = 130 = 121 + 9 = 11^2 + 3^2$

NOTES AND BACKGROUND

In his book Pillow-Problems Lewis Carroll extends this idea with
a further problem. Prove that 3 times the sum of three squares is
also the sum of 4 squares.

For further problems like this see Lewis Carroll's Games and
Puzzles compiled by Edward Wakeling published by Dover Books ISBN
0-486-26922-1.