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...

exact values. Lagrange's four-square theorem of 1770 states that every natural number is the sum of at most four squares. Since three squares are not enough...

four integer squares. As well as being an elegant theorem in its own right, Lagrange's four square theorem has useful applications in areas of mathematics...

of the three-square theorem was defective and had to be completed by Gauss. With Lagrange's four-square theorem and the two-square theorem of Girard, Fermat...

are four elementary arithmetic operations in mathematics: addition (+), subtraction (−), multiplication (×), and division (÷). Lagrange's four-square theorem...

Lagrange's theorem usually refers to any of the following theorems, attributed to Joseph Louis Lagrange: Lagrange's theorem (group theory) Lagrange's...

Legendre's three-square theorem Lagrange's four-square theorem Landau–Ramanujan constant Thue's lemma Friedlander–Iwaniec theorem D. A. Cox (1989). Primes...

series. Lagrange's four-square theorem Lambert series Sum of squares function Grosswald, Emil (1985). Representations of integers as sums of squares. Internet...

efficient approach to Fermat's theorem on sums of squares: Minkowski's theorem is also useful to prove Lagrange's four-square theorem, which states that every...

of squares of consecutive integers, see Square pyramidal number For representing an integer as a sum of squares of 4 integers, see Lagrange's four-square...

three-square theorem Lagrange's four-square theorem Sum of squares function Brahmagupta–Fibonacci identity Dudley, Underwood (1969). "Sums of Two Squares"...

four square Four-square cipher Lagrange's four-square theorem, stating that any natural number equals the sum of four integers squared Jacobi's four-square...

positive integer can be written as a sum of 4 squares, by Lagrange's four-square theorem. By the 15 theorem, to verify this, it is sufficient to check that...

formula Lagrange's identity Lagrange's identity (boundary value problem) Lagrange's mean value theorem Lagrange's notation Lagrange's theorem (group theory)...

it can be used as a basic tool for proving theorems in number theory such as Lagrange's four-square theorem and the uniqueness of prime factorizations...

In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a...

example proving Fermat's two-square theorem and Lagrange's four-square theorem, and similar results for 6 and 8 squares. His other work in number theory...

square number, while other divisors come in pairs. Lagrange's four-square theorem states that any positive integer can be written as the sum of four or...

{\displaystyle {\mathfrak {G}}^{2}=\{k^{2}\}_{k=1}^{\infty }} , then Lagrange's four-square theorem can be restated as σ ( G 2 ⊕ G 2 ⊕ G 2 ⊕ G 2 ) = 1 {\displaystyle...

theory) Lafforgue's theorem (algebraic number theory) Lagrange's four-square theorem (number theory) Landau prime ideal theorem (number theory) Lindemann–Weierstrass...

{\displaystyle S} . For example, by Lagrange's four-square theorem, the set of square numbers is an additive basis of order four, and more generally by the Fermat...

Legendre's three-square theorem characterizes the distance set of the three-dimensional integer lattice, and Lagrange's four-square theorem characterizes...

number theory can be phrased in terms of sumsets. For example, Lagrange's four-square theorem can be written succinctly in the form 4 ◻ = N , {\displaystyle...

Latin cross: it consists of four cubes stacked one on top of each other, with another four cubes attached to the exposed square faces of the second-from-top...

calculus Lagrange's trigonometric identities, two trigonometric identities Lagrange's four-square theorem, a theorem from number theory Lagrange polynomial...

Waring's problem Brahmagupta–Fibonacci identity Euler's four-square identity Lagrange's four-square theorem Taxicab number Generalized taxicab number Cabtaxi...

Joseph Louis Lagrange The Lagrange Points Derivation of Lagrange's result (not Lagrange's method) Lagrange's works (in French) Oeuvres de Lagrange, edited...

of all the positive integers is sometimes called universal. Lagrange's four-square theorem shows that w2 + x2 + y2 + z2 is universal. Ramanujan generalized...

trivially a sum of at most one natural number. Lagrange's four-square theorem says that the set of positive square numbers is an additive basis of order 4....

Fermat's little theorem, Fermat's theorem on sums of two squares, and made distinct contributions to the Lagrange's four-square theorem. He also invented...