Question

Tìm số tự nhiên n để 3n + 11 = BC(10; 2n-1).

Answer 1

=>2n-1 chia hết cho 3n+11 và 10 chia hết cho 3n+11

=>\(\left\{{}\begin{matrix}6n-3⋮3n+11\\3n+11\in\left\{1;-1;2;-2;5;-5;10;-10\right\}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}6n+22-25⋮3n+11\\3n\in\left\{-10;-12;-9;-13;-6;-16;-1;-21\right\}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3n+11\in\left\{1;-1;5;-5;25;-25\right\}\\n\in\left\{-4;-3;-2;-7\right\}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}n\in\left\{-4;-2;-12\right\}\\n\in\left\{-4;-3;-2;-7\right\}\end{matrix}\right.\Leftrightarrow n\in\left\{-4;-2\right\}\)