Chinese Remainder Theorem
The Chinese remainder theorem reconstructs an integer from compatible congruences with pairwise coprime moduli.
Definition · Example · CSE Use →Number Theory
Definitions, examples and Computer Science applications for this mathematics subject.
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Composite Number
A composite number is an integer greater than 1 that has more than two positive divisors.
Definition · Example · CSE Use →Congruence
Two integers are congruent modulo n when they have the same remainder after division by n.
Definition · Example · CSE Use →Divisibility
An integer a divides b when b can be written as a times another integer.
Definition · Example · CSE Use →Euclidean Algorithm
The Euclidean algorithm computes the greatest common divisor using repeated remainders.
Definition · Example · CSE Use →Euler’s Totient Function
Euler’s totient function φ(n) counts positive integers up to n that are coprime to n.
Definition · Example · CSE Use →Fermat’s Little Theorem
Fermat’s little theorem states that if p is prime and p does not divide a, then a^(p−1) ≡ 1 mod p.
Definition · Example · CSE Use →Greatest Common Divisor
The greatest common divisor of two integers is the largest positive integer dividing both.
Definition · Example · CSE Use →Integer
Integers include negative whole numbers, zero and positive whole numbers.
Definition · Example · CSE Use →Irrational Number
An irrational number cannot be represented as a ratio of two integers.
Definition · Example · CSE Use →Least Common Multiple
The least common multiple is the smallest positive integer divisible by each of the given integers.
Definition · Example · CSE Use →Modular Arithmetic
Modular arithmetic works with remainders after division by a modulus.
Definition · Example · CSE Use →Natural Number
Natural numbers are non-negative or positive counting numbers, depending on convention.
Definition · Example · CSE Use →Prime Number
A whole number greater than 1 with exactly two positive divisors: 1 and itself.
Definition · Example · CSE Use →Rational Number
A rational number can be written as a ratio of two integers with a non-zero denominator.
Definition · Example · CSE Use →