Question

Tìm \(n\in N\)  biết \(3n+4⋮2n+1\)

Answer 1

Ta có :

 \(\left\{{}\begin{matrix}3n+4⋮2n+1\\2n+1⋮2n+1\end{matrix}\right.\rightarrow\left\{{}\begin{matrix}2\left(3n+4\right)⋮2n+1\\3\left(2n+1\right)⋮2n+1\end{matrix}\right.\\ \rightarrow2\left(3n+4\right)-3\left(2n+1\right)⋮2n+1\\ \rightarrow5⋮2n+1\\ \rightarrow\left\{{}\begin{matrix}2n+1\inƯ\left(5\right)\\2n+1\in N\end{matrix}\right.\\ \rightarrow2n+1\in\left\{1;5\right\}\)

Vậy `n = 0` hoặc `n=2` 

Answer 2

=>6n+8 chia hết cho 2n+1

=>6n+3+5 chia hết cho 2n+1

mà n là số tự nhiên

nên \(2n+1\in\left\{1;5\right\}\)

=>\(n\in\left\{0;2\right\}\)