Đáp án:
\(\eqalign{
& a)\,\,\,\,n \in \left\{ {2;4} \right\} \cr
& b)\,\,\,\,n \in \left\{ {0;1;2;3} \right\} \cr} \)
Giải thích các bước giải:
\(\eqalign{
& a)\,\,4n - 7 = 4n - 4 - 3 = 4\left( {n - 1} \right) - 3 \cr
& 4n - 7\,\, \vdots \,\,n - 1 \Leftrightarrow - 3\, \vdots \,\,n - 1 \cr
& \Rightarrow n - 1 \in U\left( 3 \right) = \left\{ {1;3} \right\} \cr
& + )\,\,n - 1 = 1 \Leftrightarrow n = 2. \cr
& + )\,\,n - 1 = 3 \Leftrightarrow n = 4. \cr
& Vay\,\,n \in \left\{ {2;4} \right\} \cr
& b)\,\,5n - 8 = 5n - 20 + 12 = - 5\left( {4 - n} \right) + 12 \cr
& 5n - 8\,\, \vdots \,\,4 - n \Leftrightarrow 12\,\, \vdots \,\,4 - n \cr
& \Rightarrow 4 - n \in U\left( {12} \right) = \left\{ {1;2;3;4;6;12} \right\} \cr
& Do\,\,n \ge 0 \Rightarrow 4 - n \le 4 \Rightarrow 4 - n \in \left\{ {1;2;3;4} \right\} \cr
& + )\,\,4 - n = 1 \Leftrightarrow n = 3. \cr
& + )\,\,4 - n = 2 \Leftrightarrow n = 2. \cr
& + )\,\,4 - n = 3 \Leftrightarrow n = 1. \cr
& + )\,\,4 - n = 4 \Leftrightarrow n = 0 \cr
& Vay\,\,n \in \left\{ {0;1;2;3} \right\} \cr} \)
