Change superscripts to subscripts on the k

main.tex

@@ -1112,18 +1112,18 @@ Where $\epsilon_{q,1}$ and $\epsilon_{q,2}$ are defined as follows:
 
 \begin{equation*}
 	\epsilon_{q,1} :=
-	\frac{k_q^1}{2mn^2}
+	\frac{k_{q,1}}{2mn^2}
 	\qquad
 	\epsilon_{q,2} :=
-	\frac{k_q^2}{2mn^2}
+	\frac{k_{q,2}}{2mn^2}
 \end{equation*}
 \begin{align*}
 	\text{where }
-	&k_q^1 \text{ is the least }
+	&k_{q,1} \text{ is the least }
 	k\in\ZZ_{>0}\: s.t.:\:
 	k \equiv -\aa\bb m \mod n
 \\
-	&k_q^2 \text{ is the least }
+	&k_{q,2} \text{ is the least }
 	k\in\ZZ_{>0}\: s.t.:\:
 	k \equiv \aa\bb m (\aa\aa^{'}-2)
 	\mod n\gcd(2n,\aa^2 m)
@@ -1174,13 +1174,13 @@ Consider the following tautology:
 In our situation, we want to find the least $k$ satisfying 
 eqn \ref{eqn:finding_better_eps_problem}.
 Since such a $k$ must also satisfy eqn \ref{eqn:better_eps_problem_k_mod_n},
-we can pick the smallest $k_q^1 \in \ZZ_{>0}$ which satisfies this new condition
+we can pick the smallest $k_{q,1} \in \ZZ_{>0}$ which satisfies this new condition
 (a computation only depending on $q$ and $\beta$, but not $r$).
 We are then guaranteed that the gap $\frac{k}{2mn^2}$ is at least
 $\epsilon_{q,1}$.
 Furthermore, $k$ also satisfies
 eqn \ref{eqn:better_eps_problem_k_mod_gcd2n2_a2mn}
-so we can also pick the smallest $k_q^2 \in \ZZ_{>0}$ satisfying this condition,
+so we can also pick the smallest $k_{q,2} \in \ZZ_{>0}$ satisfying this condition,
 which also guarantees that the gap $\frac{k}{2mn^2}$ is at least $\epsilon_{q,2}$.
 
 \end{proof}