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Number Theory
Level
3
True or false?
Every natural number can be represented as the sum of 4 integer squares.
Yes,But not proved
None of these
No
Yes
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1 solution
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares.
p = a 0^2 + a 1^2 + a 2^2 + a 3^2\ where the four numbers a 0, a 1, a 2, a 3 are integers. For illustration, 3, 31 and 310 can be represented as the sum of four squares as follows:
3 = 1^2+1^2+1^2+0^2 31 = 5^2+2^2+1^2+1^2 310 = 17^2+4^2+2^2+1^2. This theorem was proved by Joseph Louis Lagrange in 1770.