updates

content/Math4302/Math4302_L26.md

@@ -79,7 +79,7 @@ $\phi(8)=|\{1,3,5,7\}|=4$
 
 If $[a]\in \mathbb{Z}_n^*$, then $[a]^{\phi(n)}=[1]$. So $a^{\phi(n)}\equiv 1\mod n$.
 
-#### Theorem
+#### Euler’s Theorem
 
 If $m\in \mathbb{Z}$, and $gcd(m,n)=1$, then $m^{\phi(n)}\equiv 1\mod n$.
 
@@ -104,7 +104,7 @@ Solution for $2x\equiv 1\mod 3$
 
 So solution for $2x\equiv 1\mod 3$ is $\{3k+2|k\in \mathbb{Z}\}$.
 
-#### Theorem for exsistence of solution of modular equations
+#### Theorem for existence of solution of modular equations
 
 $ax\equiv b\mod n$ has a solution if and only if $\operatorname{gcd}(a,n)|b$ and in that case the equation has $d$ solutions in $\mathbb{Z}_n$.