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In algebra, the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) [1] is an application of Euclidean division of polynomials.It states that, for every number , any polynomial is the sum of () and the product by of a polynomial in of degree less than the degree of .
Remainder theorem may refer to: Polynomial remainder theorem; Chinese remainder theorem This page was last edited on 29 December 2019, at 22:03 (UTC). Text is ...
The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain.
This is the form of the remainder term mentioned after the actual statement of Taylor's theorem with remainder in the mean value form. The Lagrange form of the remainder is found by choosing () = + and the Cauchy form by choosing () =. Remark.
In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...
Chevalley–Warning theorem (field theory) Chinese remainder theorem (number theory) Choi's theorem on completely positive maps (operator theory) Chomsky–Schützenberger enumeration theorem (formal language theory) Chomsky–Schützenberger representation theorem (formal language theory) Choquet–Bishop–de Leeuw theorem (functional analysis)
CRT – Chinese remainder theorem. csc – cosecant function. (Also written as cosec.) csch – hyperbolic cosecant function. (Also written as cosech.) ctg – cotangent function. (Also written as cot.) curl – curl of a vector field. (Also written as rot.) cvc – covercosine function. (Also written as covercos.) cvs – coversine function.
In the above theorem, each of the four integers has a name of its own: a is called the dividend, b is called the divisor, q is called the quotient and r is called the remainder. The computation of the quotient and the remainder from the dividend and the divisor is called division, or in case of ambiguity, Euclidean division.