KnowraLagrange's four-square theoremLinked fromLinked fromThe 10 pages that link to Lagrange's four-square theorem, each with the reason it gives.All 10Broader topic 3Related 2Compared with 5Joseph-Louis LagrangeBroader topic: It exemplifies his contributions to number theory beyond mechanics.Quadratic formBroader topic: It is a central example of a representation problem for a quadratic form.Additive number theoryBroader topic: This solved a landmark representation problem for sums of squares.Waring's problemRelated: It illustrates a universal representation theorem for one exponent.Euler's four-square identityRelated: Euler's identity supplies the multiplication principle used in the history of four-square results.Jacobi's four-square theoremCompared with: Lagrange proved existence; Jacobi sharpened it by counting every representation.Fermat polygonal number theoremCompared with: It is a related bounded-sum theorem, but uses squares rather than n-gonal numbers.Brahmagupta–Fibonacci identityCompared with: It concerns universal representation by four squares, not multiplicative closure of two-square forms.Legendre's three-square theoremCompared with: Unlike the three-square theorem, it has no excluded congruence classes.Lemoine's conjectureCompared with: It illustrates a representation claim that is proved for every eligible integer, unlike Lemoine's conjecture.