corrected explanation for gcd(pk, qk) = 1

src/algebra/continued-fractions.md

@@ -111,6 +111,8 @@ In the code snippets we will mostly assume finite continued fractions.
     $$
 
     Thus, computation of a continued fraction representation for $r=\frac{p}{q}$ follows the same steps as the Euclidean algorithm for $p$ and $q$.
+
+    From this connection with the Euclidean algorithm it also follows that $\gcd(p, q) = 1$ for $[a_0; a_1, \dots, a_k]$. Hence, convergents are always irreducible.
 
 === "C++"
     ```cpp