Definition 1

With the notation of Prop. 12 we say that $d$ is a greatest common divisor (gcd for short) of $f$ and $g$. We say that $f$ and $g$ are relatively prime or that $f$ is prime to $g$ if $1$ is a gcd of $f$ and $g$.

To say that $f$ and $g$ are relatively prime thus means that there exist polynomials $u$ and $v$ in $K[X]$ such that $u f + v g = 1$.