modular arithmetic

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• 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

• modular arithmetic — noun : arithmetic that deals with whole numbers where the numbers are replaced by their remainders after division by a fixed number in a modular arithmetic with modulus 5, 3 multiplied by 4 is 2 5 hours after 10 o clock is 3 o clock because… …   Useful english dictionary

• modular arithmetic — noun Date: 1959 arithmetic that deals with whole numbers where the numbers are replaced by their remainders after division by a fixed number < in a modular arithmetic with modulus 5, 3 multiplied by 4 is 2 > …   New Collegiate Dictionary

• Modular exponentiation — is a type of exponentiation performed over a modulus. It is particularly useful in computer science, especially in the field of cryptography. Doing a modular exponentiation means calculating the remainder when dividing by a positive integer m… …   Wikipedia

• Modular multiplicative inverse — The modular multiplicative inverse of an integer a modulo m is an integer x such that That is, it is the multiplicative inverse in the ring of integers modulo m. This is equivalent to The multiplicative inverse of a modulo m exists if and only if …   Wikipedia

• arithmetic — Synonyms and related words: Boolean algebra, Euclidean geometry, Fourier analysis, Lagrangian function, algebra, algebraic geometry, analysis, analytic geometry, associative algebra, binary arithmetic, calculation, calculus, ciphering, circle… …   Moby Thesaurus

• Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …   Wikipedia

• Modular form — In mathematics, a modular form is a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main… …   Wikipedia

• Modular curve — In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half plane H by the action of a congruence subgroup Γ of the modular group of …   Wikipedia

• Arithmetic mean — In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space. The term arithmetic mean is preferred in mathematics and… …   Wikipedia