English Dictionary

Farey sequence

noun

(number theory) For a given positive integer n, the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size.

The Farey sequence is a sequence of fractions between 0 and 1 that are in lowest terms and have denominators less than or equal to a given positive integer n.

意味（1）

(number theory) For a given positive integer n, the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size.

Students should then see the number of fractions N, in the Farey sequence is equal to 𝜙(2)+𝜙(3)+𝜙(4)+…+𝜙(n), where 𝜙(n) is the number of positive integers less than or equal to n that are relatively prime to n.