diff --git a/main.tex b/main.tex
index e85693c41af1e29ccd82885f090a72c7bea6ef3f..1d4bc018e03f8c82385b8846c011551f767ef34c 100644
--- a/main.tex
+++ b/main.tex
@@ -1647,20 +1647,20 @@ Consider the following:
 	\quad \text{for some } x \in \ZZ
 	\span \span \span \span \span
 	\label{eqn:finding_better_eps_problem}
-\\ &\Longleftrightarrow& 
+\\ \Longleftrightarrow& &
 	- (\aa r+2\bb)\aa
 	&\equiv k &&
 	\mod n^2
-\\ &\Longleftrightarrow&
+\\ \Longleftrightarrow& &
 	- \aa^2 r - 2\aa\bb
 	&\equiv k &&
 	\mod n^2
-\\ &\Longrightarrow&
+\\  \Longrightarrow& &
   \aa^2 \aa^{-1}\bb - 2\aa\bb
 	&\equiv k &&
 	\mod n
 	\label{eqn:better_eps_problem_k_mod_gcd2n2_a2mn}
-\\ &\Longrightarrow&
+\\ \Longleftrightarrow& &
   -\aa\bb
 	&\equiv k &&
 	\mod n