$a)$
$ A$ là số nguyên khi $ 3n+2\ \vdots 7n+1$
$\to 7(3n+2)\ \vdots 7n +1$
$\to 21n + 14 \ \vdots 7n +1$
$\to 3.(7n+1) +11 \ \vdots 7n +1$
$\to 11 \ \vdots 7n +1$
$\to 7n +1 \in Ư(11) = \{ -11 ; -1 ; 1 ; 11 \}$
$\to 7n \in \{-12 ; -2; 0; 10 \}$
$\to n \in \{ \dfrac{-12}{7} ; \dfrac{-2}{7}; 0 ; \dfrac{10}{7} \}$