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Benedict Irwin edited Rules.tex
about 9 years ago
Commit id: 70d179d952b32a90da9f5062533fee261e553872
deletions | additions
diff --git a/Rules.tex b/Rules.tex
index 5656460..f8e6172 100644
--- a/Rules.tex
+++ b/Rules.tex
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\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: If \begin{equation}
3b-a \begin{array}
\;
& (3b-a) & mod \; 7 =0
\; & \wedge
\; & n - 1 \; mod \; 6 = 0 \\
\vee
b-a \; & (b-a-4) & mod \; 7
=4 \; =0 & \wedge
\; & n - 2 \; mod \; 6 = 0 \\
\vee
3a-b \; & (3a-b) & mod \; 7 =0
\; & \wedge
\; & n - 3 \; mod \; 6 = 0 \\
\vee
b-2a \; & (b-2a-4) & mod \; 7
=4 \; =0 & \wedge
\; & n - 4 \; mod \; 6 = 0 \\
\vee
a+b \; & (a+b-3) & mod \; 7
=3 \; =0 & \wedge
\; & n - 5 \; mod \; 6 = 0 \\
\end{array} \\
\frac{Z}{7} \in \mathbb{Z}
\end{equation}