From b044fa15e82a8966f6fa55589f170f596343f2cc Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Thu, 22 Jun 2023 17:47:53 +0100
Subject: [PATCH] Improve implication arrows

---
 main.tex | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/main.tex b/main.tex
index e85693c..1d4bc01 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
-- 
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