residue class arithmetic

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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

• Modular arithmetic — In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value the modulus. The Swiss mathematician Leonhard Euler pioneered the modern… …   Wikipedia

• modular arithmetic — arithmetic in which numbers that are congruent modulo a given number are treated as the same. Cf. congruence (def. 2), modulo, modulus (def. 2b). [1955 60] * * * sometimes referred to as  modulus arithmetic  or  clock arithmetic        in its… …   Universalium

• 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

• Dirichlet's theorem on arithmetic progressions — In number theory, Dirichlet s theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n ≥ 0. In other… …   Wikipedia

• Dirichlet character — In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of . Dirichlet characters are used to define Dirichlet L functions, which are meromorphic functions with a… …   Wikipedia

• Quotient ring — In mathematics a quotient ring, also known as factor ring or residue class ring, is a construction in ring theory, quite similar to the factor groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two… …   Wikipedia

• Chebotarev's density theorem — in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic… …   Wikipedia

• List of mathematics articles (R) — NOTOC R R. A. Fisher Lectureship Rabdology Rabin automaton Rabin signature algorithm Rabinovich Fabrikant equations Rabinowitsch trick Racah polynomials Racah W coefficient Racetrack (game) Racks and quandles Radar chart Rademacher complexity… …   Wikipedia

• Multiplicative number theory — is a subfield of analytic number theory that deals with prime numbers and with factorization and divisors. The focus is usually on developing approximate formulas for counting these objects in various contexts. The prime number theorem is a key… …   Wikipedia

• Congruent number — In mathematics, a congruent number is a positive integer that is the area of a right triangle with three rational number sides.[1] A more general definition includes all positive rational numbers with this property.[2] The sequence of integer… …   Wikipedia