diff --git a/main.tex b/main.tex
index a812d2c9dbfd57efe49673d85a7f4e4aac46f656..93741a6968f4b3ef1b79e164c20edfa7402af145 100644
--- a/main.tex
+++ b/main.tex
@@ -838,6 +838,28 @@ this happens when:
 	< \frac{1}{\lcm(m,2n^2)}
 \end{equation}
 
+\begin{sagesilent}
+rhs_numerator = (
+	positive_radius_condition
+	.rhs()
+	.subs([q_value_expr,beta_value_expr])
+	.factor()
+	.numerator()
+)
+\end{sagesilent}
+
+\noindent
+Considering the numerator of the right-hand-side:
+
+\begin{align}
+	\sage{rhs_numerator}
+	&\equiv (a(-a^{-1}b)+2b)a &\mod n
+\\
+	&\equiv ab &\mod n
+\end{align}
+
+And so, we also have $a(ar+2b) \equiv ab$ (mod $\lcm(m,2n^2)$).
+
 \minorheading{Irrational $\beta$}