Question

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\(a,\dfrac{12}{3n-1}\in Z\)

\(\Rightarrow3n-1\inƯ\left(12\right)\)

\(\Rightarrow3n-1\in\left\{-12;-6;-4;-3l-2;-1;1;2;3;4;6;12\right\}\)

\(\Rightarrow n\in\left\{1;0;-1\right\}\)

b) \(\dfrac{2n+3}{7}\in Z\)

\(\Rightarrow2n+3⋮7\)

\(\Rightarrow2\left(n-2\right)+7⋮7\)

\(\Rightarrow n-2⋮7\)

\(\Rightarrow n=7k+2\left(k\in Z\right)\)