Lagrange's four-square theorem

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Lagrange's four-square theorem, also known as Bachet's conjecture, states that every nonnegative integer can be represented as a sum of four non-negative integer squares. That is, the squares form an additive basis of order four: p = a 2 + b 2 + c 2 + d 2 , {\displaystyle p=a^{2}+b^{2}+c^{2}+d^{2},} where the four numbers a , b , c , d {\displaystyle a,b,c,d} are integers. For illustration, 3, 31, and 310 can be represented as the sum of four squares as follows: 3...

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