Tìm số nguyên \[n\] biết rằng \[3n + 7\] chia hết cho \[n - 1.\]

Có \[3n + 7 = 3n - 3 + 10 = 3\left( {n - 1} \right) + 10\]

Do \[3\left( {n - 1} \right)\,\, \vdots \,\,\left( {n - 1} \right)\] nên \[10\,\, \vdots \,\,\left( {n - 1} \right)\].

Suy ra \[n - 1 \in \] Ư\[\left( {10} \right) = \left\{ { - 10\,;\,\, - 5\,;\,\, - 2\,;\,\, - 1\,;\,\,1\,;\,\,2\,;\,\,5\,;\,\,10} \right\}\]

Do đó \[n\; \in \left\{ { - 9\,;\,\, - 4\,;\,\, - 1\,;\,\,0\,;\,\,2\,;\,\,3\,;\,\,6\,;\,\,11} \right\}\].