Paper X: Universal Residual Seeds and Conditional Occupied-System Completion

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3 \node[font=\small,align=center,font=\small] at (3,4.7) {$N(a+bu)=a^2-2b^2\pmod5$};
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54 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (1.3,3.69) {$a=0$};
55 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (1.3,3.07) {$a=1$};
56 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (1.3,2.45) {$a=2$};
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62 \node[font=\small,align=center,font=\scriptsize] at (3.62,4.23) {$b=3$};
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64 \node[font=\small,align=center] at (9.6,4.25) {$u^2=2$ in $\mathbb F_{25}$};
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66 \node[font=\small,align=center] at (9.6,2) {$\#N^{-1}(0)=1$};
67 \node[font=\small,align=center] at (9.6,1.05) {$\#N^{-1}(r)=6$ for $r\ne0$};
68 \node[font=\small,align=center,font=\footnotesize] at (7,-0.1) {All 25 elements are shown. Every nonzero element is a unit.};
69 \end{tikzpicture}

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