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**theorem**due to Conway et al. (1997) which states that, if a positive definite quadratic form with integer matrix entries represents all natural numbers up to 15, then it ...Müntz's

**theorem**is a generalization of the Weierstrass approximation**theorem**, which states that any continuous function on a closed and bounded interval can be uniformly ...Plancherel's

**theorem**states that the integral of the squared modulus of a function is equal to the integral of the squared modulus of its spectrum. It corresponds to ...There are several closely related results that are variously known as the binomial

**theorem**depending on the source. Even more confusingly a number of these (and other) ...If the Taniyama-Shimura conjecture holds for all semistable elliptic curves, then Fermat's last

**theorem**is true. Before its proof by Ribet in 1986, the**theorem**had been ...Chevalley's

**theorem**, also known as the Chevalley-Waring**theorem**, states that if f is a polynomial in F[x_1,...,x_n], where F is a finite field of field characteristic p, and ...For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The

**theorem**can ...Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's

**theorem**states that the two ...If the vertices A, B, and C of triangle DeltaABC lie on sides QR, RP, and PQ of the triangle DeltaPQR, then the three circumcircles CBP, ACQ, and BAR have a common point X. ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

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