Relatively prime

Two positive integers ${m}$ and ${n}$ are said to be relatively prime or coprime if they share no common divisors greater than 1. Equivalently, ${m}$ and ${n}$ must have no prime divisors in common, which is mathematically written $\gcd(m,n)=1$ . The positive integers ${m}$ and ${n}$ are relatively prime if and only if $\frac{m}{n}$ is in lowest terms.

Number Theory

Relatively prime numbers show up frequently in number theory formulas and derivations:

Euler's totient function determines the number of positive integers less than any given positive integer that are relatively prime to that number.

By the Euclidean algorithm, consecutive positive integers are always relatively prime. This is related to the fact that two numbers $a$ and $b$ are relatively prime if and only if there exist some ${x},{y}\in \mathbb{Z}$ such that $ax+by=1$ .

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Relatively prime

Number Theory

See also