Question

Tìm n, biết n \(\in\)Z và 2n - 1 chia hết cho n+1

Answer 1

2n -1 chai hết cho n + 1

\(\Rightarrow\) \(\left(n+1+n+1-3\right)\) chia hết cho n + 1

\(\Rightarrow\) 3 chia hết cho n + 1

\(\Rightarrow n+1\inƯ\left(3\right)\)

Mà \(Ư\left(3\right)=\left\{1;-1;3;-3\right\}\)

\(\Rightarrow n+1\in\left\{1;-1;3;-3\right\}\)

\(\Rightarrow n\in\left\{0;-2;2;-4\right\}\)

Answer 2

ta có : 2n-1=2(n+1)-3

Nếu 2n-1 chia hết cho n+1 => 2(n+1)-3 chia hết cho n+1 => 3 chia hết cho n+1

=> n+1 thuộc Ư(3)=> n+1 thuộc {1,-1,3,-3}Ư => n thuộc {0,-2,2,-4}

Answer 3

\(2n-1⋮n+1\Rightarrow2\left(n+1\right)-1-2⋮\left(n+1\right)\)

\(\Rightarrow2\left(n+1\right)-3⋮\left(n+1\right).\)Vì \(2\left(n+1\right)⋮\left(n+1\right)\)nên\(3⋮n+1\)

\(\Rightarrow n+1\inƯ\left(3\right)=\left\{\pm1,\pm3\right\}\)

\(\Rightarrow n\in\left\{0,-2,2,-4\right\}\)