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Update arithmetics-moonmath.tex #118

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2 changes: 1 addition & 1 deletion chapters/arithmetics-moonmath.tex
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Expand Up @@ -778,7 +778,7 @@ \subsection{Modular Inverses}
3x+3+3 &= 3 & \text{\# addition-table: } 3+3 = 0 \\
3x &= 3 & \text{\# division not possible (no multiplicative inverse of 3 exists)}
\end{align*}
So, in this case, we cannot solve the equation for $x$ by dividing by $3$. And, indeed, when we look at the multiplication table of $\Z_6$ (\examplename{} \ref{def_residue_ring_z_6}), we find that there are three solutions $x\in\{1,3,5\}$, such that $3x+3=0$ holds true for all of them.
So, in this case, we cannot solve the equation for $x$ by dividing by $3$. And, indeed, when we look at the multiplication table of $\Z_6$ (\examplename{} \ref{def_residue_ring_z_6}), we find that there are three solutions $x\in\{1,3,5\}$, such that $3x-3=0$ holds true for all of them.
\end{example}
\begin{exercise}
Consider the modulus $n=24$. Which of the integers $7$, $1$, $0$, $805$, $-4255$ have multiplicative inverses in modular $24$ arithmetic? Compute the inverses, in case they exist.
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