residue (number) system

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• Residue number system — A residue number system (RNS) represents a large integer using a set of smaller integers, so that computation may be performed more efficiently. It relies on the Chinese remainder theorem of modular arithmetic for its operation, a mathematical… …   Wikipedia

• Covering system — In mathematics, a covering system (also called a complete residue system) is a collection of finitely many residue classes whose union covers all the integers. Unsolved problems in mathematics For any arbitrarily large natural number N does there …   Wikipedia

• Numeral system — This article is about different methods of expressing numbers with symbols. For classifying numbers in mathematics, see number system. For how numbers are expressed using words, see number names. Numeral systems by culture Hindu Arabic numerals… …   Wikipedia

• List of number theory topics — This is a list of number theory topics, by Wikipedia page. See also List of recreational number theory topics Topics in cryptography Contents 1 Factors 2 Fractions 3 Modular arithmetic …   Wikipedia

• Reduced residue system — A reduced residue system modulo n is a set of phi( n ) integers such that each integer is relatively prime to n and no two are congruent modulo n . Here phi denotes Euler s totient function.Facts*If { r 1, r 2, dots, r {varphi(n)} } is a reduced… …   Wikipedia

• Number theory — A Lehmer sieve an analog computer once used for finding primes and solving simple diophantine equations. Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers (the… …   Wikipedia

• P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …   Wikipedia

• p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… …   Wikipedia

• Quadratic residue — In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… …   Wikipedia

• Winding number — The term winding number may also refer to the rotation number of an iterated map. This curve has winding number two around the point p. In mathematics, the winding number of a closed curve in the plane around a given point is an integer… …   Wikipedia

• Class number formula — In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function Contents 1 General statement of the class number formula 2 Galois extensions of the rationals 3 A …   Wikipedia