In 1770, Lagrange proved that any prime number

*p*can be written as a sum of four (integer) squares:

By making use of this fact and Euler's previous discovery (see this previous post of mine) that the product of sums of four squares can be written as a sum of four squares, Lagrange has now proved that every positive integer can be written as a sum of four squares. For example,

2012 = 44^2 +6^2 +6^2 +2^2

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