Benedict Irwin edited Rules.tex  about 9 years ago

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\end{equation}  These matrices may be generated by the rules \begin{equation}  \begin{array}  \Theta_1 :\; :&  if \; 3b-a \; & (3b-a) &  mod \; 7 = 0 \\ \Theta_2 :\; :&  if \; b-a \; & (b-a) &  mod \; 7 = 4 \\ \Theta_3 :\; :&  if \; 3a-b \; & (3a-b) &  mod \; 7 = 0 \\ \Theta_4 :\; :&  if \; b-2a \; & (b-2a) &  mod \; 7 = 4 \\ \Theta_5 :\; :&  if \; a+b \; & (a+b) &  mod \; 7 = 3 \\ \end{array}  \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}