\(\text{a) }(5n+4)\ \vdots\ n\)
\(\text{Ta có: }5n\ \vdots\ n \Rightarrow 4\ \vdots\ n\)
\(\Rightarrow n \in Ư(4)\)
\(Ư(4)=\{\pm1;\pm2;\pm4\}\)
\(\Rightarrow n\in \{\pm1;\pm2;\pm4\}\)
\(\text{b) }(n+6)\ \vdots\ (n+2)\)
\(\Rightarrow (n+2+4)\ \vdots\ (n+2)\)
\(\text{Ta có: }(n+2)\ \vdots\ (n+2)\Rightarrow 4\ \vdots\ (n+2)\)
\(\Rightarrow (n+2)\in Ư(4)\)
\(Ư(4)=\{\pm1;\pm2;\pm4\}\)
\((n+2)\in\{\pm1;\pm2;\pm4\}\)
\(\text{Lập bảng:}\)
| \(n+2\) |
\(-4\) |
\(-2\) |
\(-1\) |
\(1\) |
\(2\) |
\(4\) |
| \(n\) |
\(-6\) |
\(-4\) |
\(-3\) |
\(-1\) |
\(0\) |
\(2\) |
\(\text{Vậy }n=\{-6;-4;-3;-1;0;2\}\)
\(\text{c) }(3n+1)\ \vdots\ (n-2)\)
\(\Rightarrow (3n-6+7)\ \vdots\ (n-2)\)
\(\Rightarrow [(3n-6)+7]\ \vdots\ (n-2)\)
\(\Rightarrow [3(n-2)+7]\ \vdots\ (n-2)\)
\(\text{Ta có: }3(n-2)\ \vdots\ (n-2)\Rightarrow 7\ \vdots\ (n-2)\)
\(\Rightarrow (n-2)\in Ư(7)\)
\(Ư(7)=\{\pm1;\pm7\}\)
\((n-2)\in \{\pm1;\pm7\}\)
\(\text{Lập bảng:}\)
| \(n-2\) |
\(-7\) |
\(-1\) |
\(1\) |
\(7\) |
| \(n\) |
\(-5\) |
\(1\) |
\(3\) |
\(9\) |
\(\text{Vậy }n=\{-5;1;3;9\}\)
\(\text{d) }(3n+9)\ \vdots\ (2n-1)\)
\(\Rightarrow 2(3n+9)\ \vdots\ (2n-1)\)
\(\Rightarrow (6n+18)\ \vdots\ (2n-1)\)
\(\Rightarrow (6n-3+21)\ \vdots\ (2n-1)\)
\(\Rightarrow [(6n-3)+21]\ \vdots\ (2n-1)\)
\(\Rightarrow [3(2n-1)+21]\ \vdots\ (2n-1)\)
\(\text{Ta có: }3(2n-1)\ \vdots\ (2n-1)\Rightarrow 21\ \vdots\ (2n-1)\)
\(\Rightarrow (2n-1)\in Ư(21)\)
\(Ư(21)=\{\pm1;\pm3;\pm7;\pm21\}\)
\((2n-1)\in\{\pm1;\pm3;\pm7;\pm21\}\)
\(\text{Lập bảng:}\)
| \(2n-1\) |
\(-21\) |
\(-7\) |
\(-3\) |
\(-1\) |
\(1\) |
\(3\) |
\(7\) |
\(21\) |
| \(n\) |
\(-10\) |
\(-3\) |
\(-1\) |
\(0\) |
\(1\) |
\(2\) |
\(4\) |
\(11\) |
\(\text{Vậy }n=\{-10;-3;-1;0;1;2;4;11\}\)
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