Theorem

Lagrange's Four-Square Theorem

Number Theory

Every natural number can be represented as the sum of four integer squares. The theorem is a landmark result in additive number theory and a special case of Waring's problem for the exponent two.

Facts

Statement

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. 1

Proof Year

1770 1

Classification

Statement Form

Existence Theorem 1

Connections

Sources

1. Lagrange's Four-Square Theorem (Wikipedia)

Wikimedia Foundation

lead section, first paragraph
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.
History section
This theorem was proven by Joseph-Louis Lagrange in 1770.

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Lagrange's Four-Square Theorem

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