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Four-squares theorem

The four-squares theorem reads:

Any positive integer can be written as the sum of four squares of integers.

 


Explanation

For small numbers it is not difficult to determine, because

3 = 1 + 1 + 1 + 0

31 = 25 + 4 + 1 + 0

310 = 289 + 16 + 4 + 1

 


Additional information

The theorem was proven in 1770 by Joseph-Louis Lagrange.

 


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