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A theorem also known as Bachet's Conjecture which was stated but not proven by Diophantus. It states that every
Positive Integer can be written as the Sum of at most four Squares. Although
the theorem was proved by Fermat 
using infinite descent, the proof was suppressed. Euler was unable
to prove the theorem. The first published proof was given by Lagrange in 1770 and made use of the Euler
Four-Square Identity.
See also Euler Four-Square Identity, Fermat's Polygonal Number Theorem, Fifteen Theorem, Vinogradov's Theorem, Waring's Problem