Question

Tìm số tự nhiên n sao cho 4n-5 chia hết cho 2n-1

Giúp mk với

Answer 1

\((4n-5) \ \vdots \ (2n-1) \\\Leftrightarrow [2(2n-1)-3] \ \vdots \ (2n-1) \\\Leftrightarrow 3 \ \vdots \ (2n-1) \\\Leftrightarrow (2n-1)\in Ư(3)\)

Mà \(n\in \mathbb{N}\Rightarrow 2n-1\ge -1\)

\(\Rightarrow (2n-1)\in \{ -1;1;3 \} \\\Rightarrow n\in \{ 0;1;2 \}\)

Vậy...

Answer 2

Ta có:

\(4n-5⋮2n-1\)

\(\Rightarrow\left(4n-2\right)-3⋮2n-1\)

\(\Rightarrow2\left(2n-1\right)-3⋮2n-1\)

\(\Rightarrow-3⋮2n-1\)

\(\Rightarrow2n-1\in\left\{1;3\right\}\) ( vì \(n\in N\) )

\(\Rightarrow\left\{{}\begin{matrix}2n-1=1\Rightarrow n=1\\2n-1=3\Rightarrow n=2\end{matrix}\right.\)

Vậy \(n\in\left\{1;2\right\}\)