Benedict Irwin edited Rules.tex  about 9 years ago

Commit id: 70d179d952b32a90da9f5062533fee261e553872

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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}