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Benedict Irwin edited Rules.tex
about 9 years ago
Commit id: d7eff1b5995b645cc1327c55c1cf9aa51b7e4198
deletions | additions
diff --git a/Rules.tex b/Rules.tex
index 1909239..d125381 100644
--- a/Rules.tex
+++ b/Rules.tex
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\Theta_2 :\; if \; b-a \; mod \; 7 = 4 \\
\Theta_3 :\; if \; 3a-b \; mod \; 7 = 0 \\
\Theta_4 :\; if \; b-2a \; mod \; 7 = 4 \\
\Theta_5 :\; if \; a+b \; mod \; 7 = 3
\\
\end{equation}
This provides the general rule for divisibility by $7$,
for an integer $Z=1|a;n|1|b;n|1$, $\forall a,b,n$ as:
\begin{equation} If
\; \begin{equation}
3b-a \; mod \; 7 =0 \;
then \; if \wedge \; n - 1 \; mod \; 6 = 0 \\
If \; \vee b-a \; mod \; 7 =4 \;
then \; if \wedge \; n - 2 \; mod \; 6 = 0 \\
If \; \vee 3a-b \; mod \; 7 =0 \;
then \; if \wedge \; n - 3 \; mod \; 6 = 0 \\
If \; \vee b-2a \; mod \; 7 =4 \;
then \; if \wedge \; n - 4 \; mod \; 6 = 0 \\
If \; \vee a+b \; mod \; 7 =3 \;
then \; if \wedge \; n - 5 \; mod \; 6 = 0
\\
frac{Z}{7} \in \mathbb{Z}
\end{equation}