Historical Development
The theorem appears in the Arithmetica of Diophantus, translated into Latin by Bachet in 1621.
Adrien-Marie Legendre improved on the theorem in 1798 by stating that a positive integer can be expressed as the sum of three squares if and only if it is not of the form 4k(8m + 7). His proof was incomplete, leaving a gap which was later filled by Carl Friedrich Gauss.
Read more about this topic: Lagrange's Four-square Theorem
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