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Modulo is a mathematical operation that returns the remainder of a division. In computing, different systems and languages have different ways of defining and implementing modulo, depending on the signs and types of the operands.
Learn about modular arithmetic, a system of arithmetic for integers where numbers "wrap around" when reaching a certain value, called the modulus. Find out how modular arithmetic is used in various fields of mathematics, such as number theory, cryptography, and computer science.
Modulo is a term that means two objects are equivalent up to a certain factor. It is used in various contexts of mathematics, such as modular arithmetic, group theory, ring theory, and computing.
Learn about the law of quadratic reciprocity, a theorem in number theory that gives conditions for the solvability of quadratic equations modulo prime numbers. See examples, proofs, applications, and generalizations of this fundamental result.
Learn about the group of integers coprime to n under multiplication modulo n, denoted by or . Find out its order, structure, generators, and applications in number theory and cryptography.
Learn about the conditions and theorems for solving the congruence x3 ≡ p (mod q) in number theory. Find out how mod p, cubic residues, and cubic characters are related to Fermat, Gauss, Jacobi, and Lehmer.
A modular multiplicative inverse of an integer a is an integer x such that ax is congruent to 1 modulo m. Learn how to find, use and apply this concept in arithmetic, cryptography and number theory.
The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or ...