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Benedict Irwin edited Rules.tex
almost 9 years ago
Commit id: e1b9c15df5cb490ff65f60f6f4374be5711a1138
deletions | additions
diff --git a/Rules.tex b/Rules.tex
index ed29d45..0831dcc 100644
--- a/Rules.tex
+++ b/Rules.tex
...
\end{array} \\
\frac{Z}{11} \in \mathbb{Z}
\end{equation}
Or rather more succinctly as: If \begin{equation}
(a+b-3)\; \mathrm{mod} \; 11 =0 \wedge n-1 \; \mathrm{mod} \; 2 = 0
\end{equation}
\section{13}
For divisibility by $13$, the general $\Gamma$ matrix can be constructed below
...
\end{equation}
Here we can see that if a number occurs, then that number plus $6$ also occurs if it is still in the range modulo $[1,12]$.
\begin{equation}
\Theta_{1}= \Theta_{1}\to\Theta_{7}=
\begin{bmatrix}
1 & & & & & & & & & \\
& & & &1 & & & & & \\
...
\end{bmatrix}
\end{equation}
\begin{equation}
\Theta_{2}= \Theta_{2}\to\Theta{8}=
\begin{bmatrix}
& &2 & & & & & & & \\
& & &2 & & & & & & \\
...
\end{bmatrix}
\end{equation}
\begin{equation}
\Theta_{4}= \Theta_{4}\to\Theta{10}=
\begin{bmatrix}
& & & & & & & & & \\
& & & & & & & &4 & \\
...
\end{bmatrix}
\end{equation}
Leaving Rules
\begin{equation}
\begin{array}
\; & [(a+3b) & mod \; 13 =0 & \wedge & n - 1 \; mod \; 6 = 0] \\ % 1 & 7
\vee & [(b-a-1) & mod \; 13 =0 & \wedge & n - 2 \; mod \; 6 = 0] \\ % 2 & 8
\vee & [(a+b-3) & mod \; 13 =0 & \wedge & n - 5 \; mod \; 6 = 0] \\ % 5 & 11
\end{array} \\
\frac{Z}{13} \in \mathbb{Z}
\end{equation}
\section{17}
For divisibility by $17$, the general $\Gamma$ matrix can be constructed below
\begin{equation}
...