We know that if $\gcd(a,b)$ is equal to $1,$ then they are relatively prime.
However, I have seen all pairs $(a,b)$ as positive integers. My question is can any pair $(a,b)$ of negative integers be relatively prime?
For example, are $(-1,-1)$ and $(-18,-5)$ relatively prime?
Best Answer
We may define relatively prime integers as follows.
Two integers are relatively prime if they do not have any common prime factors.
For example $5$ and $-12$ are relatively prime because the only prime factor of $5$ is $5$ which is not a facotor of $-12$ whose prime factors are $2$ and $3$.