Coprimality

https://en.wikipedia.org/wiki/Coprime_integers

Two integers are coprime if they have no common factors (beside 1), or, equivalently, if their gcd is 1.

A set of integers, e.g. A = {3, -7, 1}, is relatively prime if there is no integer d > 1 (i.e. d ∈ ℕᐩᐩ), such that d divides all of them.

Relatively Prime is also called "coprime" or "mutually prime".

¬∃x ∈ ℕᐩᐩ. ∀a ∈ A ⊆ ℤ. x ∤ a ...then a's are relatively prime

A set of integers is coprime if no integer d > 1 divides any pair of them.

Therefore, for any two integers these two definitions coincide, but for a larger collection, the property of coprimality is stronger because a set of integers can be relatively prime but not coprime, e.g. (6, 15, -5).

The coprime relation is a relation between (two) integers. It can also be considered a constraint on a set of integers.

Linguistics

• coprimeness or coprimality Property/quality/condition of being coprime

• The word "coprime", alternatively spelled "co-prime" is a non-comparable adjective. In math, adjectives can be used in phrases like "A and B are coprime", "A is coprime to B", or less commonly, "A is coprime with B".

• (number theory) "coprime" may be used to relate two or more natural numbers as having no natural number factors in common (besides 1), as in "24 and 35 are coprime".

• (number theory) "coprime" may be used to qualify a natural number having no natural number factors (except for 1) in common with some other natural numbers, as in "10 is coprime to 19".

• (algebra) by extension from number theory, one can speak of two or more polynomials whose gcd is a nonzero constant (a polynomial of degree 0).