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  2. Polynomial remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Polynomial_remainder_theorem

    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 of and a polynomial in of degree one less than the degree of .

  3. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    The theorem which underlies the definition of the Euclidean division ensures that such a quotient and remainder always exist and are unique. [20] In Euclid's original version of the algorithm, the quotient and remainder are found by repeated subtraction; that is, r k−1 is subtracted from r k−2 repeatedly until the remainder r k is smaller ...

  4. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    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)

  5. Remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Remainder_Theorem

    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 ...

  6. Euclidean division - Wikipedia

    en.wikipedia.org/wiki/Euclidean_division

    In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...

  7. List of terms relating to algorithms and data structures

    en.wikipedia.org/wiki/List_of_terms_relating_to...

    The NIST Dictionary of Algorithms and Data Structures [1] is a reference work maintained by the U.S. National Institute of Standards and Technology.It defines a large number of terms relating to algorithms and data structures.

  8. Ruffini's rule - Wikipedia

    en.wikipedia.org/wiki/Ruffini's_rule

    Ruffini's rule can be used when one needs the quotient of a polynomial P by a binomial of the form . (When one needs only the remainder, the polynomial remainder theorem provides a simpler method.) A typical example, where one needs the quotient, is the factorization of a polynomial p ( x ) {\displaystyle p(x)} for which one knows a root r :

  9. Chinese remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Chinese_remainder_theorem

    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.