Remainder theorem information

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 articles associated with the title...

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

division of integers and leads to polynomial remainders. Its existence is based on the following theorem: Given two univariate polynomials a(x) and b(x)...

Euclidean division theorem. In general, an existence proof does not provide an algorithm for computing the existing quotient and remainder, but the above...

numbers that satisfy multiple congruences according to the Chinese remainder theorem, to construct continued fractions, and to find accurate rational approximations...

of synthetic division is useful in the context of the polynomial remainder theorem for evaluating univariate polynomials. To summarize, the value of...

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

x_{2}=x_{1}+kv,\quad y_{2}=y_{1}-ku,} which completes the proof. The Chinese remainder theorem describes an important class of linear Diophantine systems of equations:...

the form x ≡ k (mod a) and x ≡ m (mod b), has a solution (Chinese remainder theorem); in fact the solutions are described by a single congruence relation...

important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special...

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

resulting scheme is equivalent to Shamir's polynomial system. The Chinese remainder theorem can also be used in secret sharing, for it provides us with a method...

the construction of the profinite integers is by using the Chinese remainder theorem. Recall that for an integer n {\displaystyle n} with prime factorization...

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

In algebraic group theory, approximation theorems are an extension of the Chinese remainder theorem to algebraic groups G over global fields k. Eichler...

Vedic sources, though there is some algebra in each. The Chinese remainder theorem appears as an exercise in Sunzi Suanjing (3rd, 4th or 5th century...

isomorphic to the direct product of these rings. For example, the Chinese remainder theorem may be stated as: if m and n are coprime integers, the quotient ring...

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...

isomorphism. These statements are equivalent as a result of the Chinese remainder theorem, which implies that Z j k ≅ Z j ⊕ Z k {\displaystyle \mathbb {Z} _{jk}\cong...

telnet client .crt, X.509 Certificate filename extension Chinese remainder theorem, in number theory Crater (constellation), in astronomy (abbreviated...