Question

21 pe 3a+1 = ..................?

Answer 1

$\frac{21}{3a+1} \in N \ \ => (3a+1)|21 \\\\\\ 3a+1 \in \{1;3;7;21 \} \\\\ 1) 3a+1=1 <=> 3a=0 \to\boxed{a=0} \\\\ 2)3a+1=3<=>3a=2 \to a=\frac{2}{3} \\\\ 3)3a+1=7<=>3a=6 \to \boxed{a=2} \\\\ 4)3a+1=21<=>3a=20 \to a=\frac{20}{3} \\\\\\ \boxed{\boxed{S\in \{0;2 \}}}$