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Coprime integers

In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also a is prime to b or a is coprime with b.

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Notation and testing

Properties

Coprimality in sets

Probability of coprimality

Generating all coprime pairs

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Coprime integers

Nodes63
Edges62
Triples6
Avg. degree1.97
Density0.031746
Components1

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Important terminology

coprime integers displaystyle prime two number probability numbers integer set positive one divisor common also pairwise pair relatively divides ring

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
binary GCD algorithm or Lehmer's GCD algorithm.The number of integers coprime with a positive integer ninstance ofA fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants0.80text
between 1instance ofA fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants0.80text
ninstance ofA fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants0.80text
is given by Euler's totient functioninstance ofA fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants0.80text
also known as Euler's phi functioninstance ofA fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants0.80text
φinstance ofA fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants0.80text

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