a) \(21⋮\left(n-1\right)\Rightarrow\left(n-1\right)\inƯ\left(21\right)\)
\(\Rightarrow\left(n-1\right)\in\left\{1;3;7;21\right\}\)
\(\Rightarrow n\in\left\{2;4;8;22\right\}\)
b)\(55⋮\left(2n-1\right)\Rightarrow\left(2n-1\right)\inƯ\left(55\right)\)
\(\Rightarrow\left(2n-1\right)\in\left\{1;5;11;55\right\}\)
\(\Rightarrow2n\in\left\{2;6;12;56\right\}\)
\(\Rightarrow n\in\left\{1;3;6;28\right\}\)
c) \(\frac{n+3}{n-1}=\frac{n-1+4}{n-1}=\frac{n-1}{n-1}+\frac{4}{n-1}=1+\frac{4}{n-1}\)
Vì \(1\in N\Rightarrow4⋮\left(n-1\right)\)
\(\Rightarrow\left(n-1\right)\inƯ\left(4\right)\)
\(\Rightarrow\left(n-1\right)\in\left\{1;2;4\right\}\)
\(\Rightarrow n\in\left\{2;3;5\right\}\)
d) \(\frac{2n+1}{n-1}=\frac{2n-2+3}{n-1}=\frac{2.\left(n-1\right)+3}{n-1}\)\(=\frac{2.\left(n-1\right)}{n-1}+\frac{3}{n-1}=2+\frac{3}{n-1}\)
Vì \(2\in N\Rightarrow3⋮\left(n-1\right)\Rightarrow n-1\inƯ\left(3\right)\)
\(\Rightarrow n-1\in\left\{1;3\right\}\)
\(\Rightarrow n\in\left\{2;4\right\}\)
