the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) is an application of Euclidean division of polynomials. It states...

In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then...

Remainder theorem may refer to: Polynomial remainder theorem Chinese remainder theorem This disambiguation page lists mathematics articles associated with...

redundancy check uses the remainder of polynomial division to detect errors in transmitted messages. Polynomial remainder theorem Synthetic division, a more...

{\displaystyle a} is a root of the polynomial). The theorem is a special case of the polynomial remainder theorem. The theorem results from basic properties...

(integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo operation...

fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with...

univariate polynomial p is a sequence of polynomials associated with p and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses...

Integer-valued polynomial Algebraic equation Factor theorem Polynomial remainder theorem See also Theory of equations below. Polynomial ring Greatest common...

is, b(x) = x − c for some constant c, then the polynomial remainder theorem asserts that the remainder of the division of a(x) by b(x) is the evaluation...

(R(x)) polynomial, the degree of which is one less than that of P(x). The final value obtained, s, is the remainder. The polynomial remainder theorem asserts...

calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree k {\textstyle...

following theorem: Given two univariate polynomials a and b ≠ 0 defined over a field, there exist two polynomials q (the quotient) and r (the remainder) which...

q(x) is some quotient polynomial and r(x) is a remainder polynomial such that 0 ≤ deg r(x) < n. By the Cayley–Hamilton theorem, replacing x by the matrix...

a system of simultaneous polynomial congruences, and may be solved by means of the Chinese remainder theorem for polynomials. Birkhoff interpolation is...

theorem (abstract algebra) Joubert's theorem (algebra) Lagrange's theorem (number theory) Mason–Stothers theorem (polynomials) Polynomial remainder theorem...

division theorem can be generalized to univariate polynomials over a field and to Euclidean domains. In the case of univariate polynomials, the main...

= P mod m 1 {\displaystyle R_{1}=P{\bmod {m}}_{1}} using the Polynomial remainder theorem, which can be done in O ( n log ⁡ n ) {\displaystyle O(n\log...

consequence of the polynomial remainder theorem, the entries in the third row are the coefficients of the second-degree polynomial, the quotient of f...

especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers...

division is useful in the context of the polynomial remainder theorem for evaluating univariate polynomials. To summarize, the value of p ( x ) {\displaystyle...

1922. Theorem 1 (Schwartz, Zippel). Let P ∈ R [ x 1 , x 2 , … , x n ] {\displaystyle P\in R[x_{1},x_{2},\ldots ,x_{n}]} be a non-zero polynomial of total...

Bézout's lemma), named after Étienne Bézout who proved it for polynomials, is the following theorem: Bézout's identity—Let a and b be integers with greatest...

Chinese remainder theorem. Instead of checking for remainders of integers modulo prime numbers, we are checking for remainders of polynomials when divided...

Stronger forms of the theorem state that the sum of the reciprocals of these prime values diverges, and that different linear polynomials with the same ⁠ b...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

factors. Polynomials with coefficients in the integers or in a field possess the unique factorization property, a version of the fundamental theorem of arithmetic...

stated the theorem for the cases of a + nd, where a = 1. This special case of Dirichlet's theorem can be proven using cyclotomic polynomials. The general...