---- > [!definition] Definition. ([[relatively prime integers]]) > Let $a,b \in \zz \cut \{ 0 \}$. If [[greatest common divisor]]$(a,b)=1$, we say $a$ and $b$ are **relatively prime** or **coprime**. > \ **Remark**. As a corollary of [[GCD is a linear combination]], $a$ and $b$ are coprime if and only if there exist $s,t \in \zz$ s.t. $as+bt=1$. > >More generally, we call two [[ideal|ideals]] $I_{1}$, $I_{2}$ of a [[ring]] $R$ **coprime** if $I_{1}+I_{2}=(1)$. ^9a006d ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```