residue arithmetic

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• Residue — may refer to: * Residue (chemistry), material remaining after a distillation or an evaporation, or portion of a larger molecule * Residue (law), portion of the testator s estate that is not specifically devised to someone in the will * Residue… …   Wikipedia

• 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 — 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

• 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

• 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

• Noncommutative residue — In mathematics, noncommutative residue, defined independently by M. Wodzicki (1984) and Guillemin (1985), is a certain trace on the algebra of pseudodifferential operators on a compact differentiable manifold that is expressed via a local density …   Wikipedia

• Aryabhata algorithm — is an algorithm to solve indeterminate Diophantine equations and for residue arithmetic. It is first described in the mathematician astronomer Aryabhata s book Aryabhatiya (499).In recent years, it has been used for cryptographic… …   Wikipedia

• RAAP — biomed. abbr. Radford Army Ammunition Plant comp. abbr. Residue Arithmetic Associative Processor comp. abbr. Resource Allocation and Planning milit. abbr. Radford Army Ammunition Plant …   United dictionary of abbreviations and acronyms

• Quadratic reciprocity — The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which shows a remarkable relationship between the solvability of certain quadratic equations modulo different prime moduli.Although it allows us to… …   Wikipedia

• Montgomery reduction — In arithmetic computation, Montgomery reduction is an algorithm introduced in 1985 by Peter Montgomery that allows modular arithmetic to be performed efficiently when the modulus is large (typically several hundred bits). A single application of… …   Wikipedia