Relatively prime

Revision as of 04:13, 20 June 2006 by ZetaX (talk | contribs)

(Also called coprime.)

Two relatively prime integers ${m}$ and ${n}$ share no common factors, so their $\gcd$ is $1$. Alternatively, ${m}$ and ${n}$ must have no prime factors in common. For example, 15 and 14 are relatively prime; as the prime factorization of 15 is $3 \cdot 5$, the prime factorization of 14 is $2 \cdot 7$, and no prime factors are shared between the two.

Note that for relatively prime ${m}$ and ${n}$, $\frac{m}{n}$ will be in lowest terms.

Relatively prime numbers show up frequently in number theory formulas and derivations. Euler's totient function, for example, determines the number of positive integers less than any given positive integer that are relatively prime to that number. The Chicken mcNugget theorem also involves relatively prime numbers.

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