Lagrange's four-square theorem, also known as Bachet's conjecture, states that any natural number can be represented as the sum of four integer squares
where the four numbers a0, a1, a2, a3 are integers. For illustration, 3, 31 and 310 can be represented as the sum of four squares as follows:
- 3 = 12 + 12 + 12 + 02
- 31 = 52 + 22 + 12 + 12
- 310 = 172 + 42 + 22 + 12.
This theorem was proven by Joseph Louis Lagrange in 1770, and corresponds to Fermat's theorem on sums of two squares.
Read more about Lagrange's Four-square Theorem: Historical Development, Proof Using The Hurwitz Integers, Generalizations, Algorithms, Uniqueness
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