Ta có:
\(P=\frac{2n-1}{n-1}\)
Để P là số nguyên.
\(\Rightarrow\frac{2n-1}{n-1}\) là số nguyên.
\(\Rightarrow2n-1⋮n-1\)
\(\Rightarrow2n-2+1⋮n-1\)
\(\Rightarrow2.\left(n-1\right)+1⋮n-1\)
Vì \(2.\left(n-1\right)⋮n-1.\)
\(\Rightarrow1⋮n-1\)
\(\Rightarrow n-1\inƯC\left(1\right)\)
\(\Rightarrow n-1\in\left\{1;-1\right\}.\)
\(\Rightarrow\left[{}\begin{matrix}n-1=1\\n-1=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}n=1+1\\n=\left(-1\right)+1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}n=2\left(TM\right)\\n=0\left(TM\right)\end{matrix}\right.\)
Vậy \(n\in\left\{2;0\right\}.\)
Chúc bạn học tốt!
