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
StatementLagrange'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 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proved By
Sources
1. Lagrange's Four-Square Theorem (Wikipedia)
Wikimedia Foundationlead 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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