coprime

Adjective

Meaning

(number theory, of two or more positive integers) Having no positive integer factors in common, aside from 1.
24 and 35 are coprime.

(number theory, of a positive integer) Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.
24 is coprime to 35.

(algebra, by extension, of two or more polynomials) Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).

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Examples

A set of integers can also be called coprime if its elements share no common positive factor except 1. A set of integers is said to be pairwise coprime if a and b are coprime for every pair (a, b) of different integers in it. Source: Internet

Also, a pair of coprime amicable numbers cannot be generated by Thabit's formula (above), nor by any similar formula. Source: Internet

Case of two moduli We want to solve the system : where and are coprime. Source: Internet

Equivalently, n is prime if and only if all integers m satisfying 2 ≤ m ≤ n − 1 are coprime to n, i.e. their only common divisor is one. Source: Internet

For a fixed value of n it is multiplicative in q: :If q and r are coprime, Many of the functions mentioned in this article have expansions as series involving these sums; see the article Ramanujan's sum for examples. Source: Internet

For this, let us consider k monic polynomials of degree one: : They are pairwise coprime if the are all different. Source: Internet

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