Để \(P=\dfrac{2n-1}{n-1}\in Z\)
Thì \(2n-1⋮n-1\)
\(\Leftrightarrow\left(2n-2\right)+1⋮n-1\)
\(\Leftrightarrow2\left(n-1\right)+1⋮n-1\)
\(\Leftrightarrow1⋮n-1\)
\(\Leftrightarrow n-1\in U\left(1\right)=\left\{-1;1\right\}\)
\(\Leftrightarrow n\in\left\{0;2\right\}\)
Vậy \(n\in\left\{0;2\right\}\) thì \(P\in Z\)