Question

tìm số tự nhiên n sao cho 13n chia hết cho n-1

Answer 1

\(\dfrac{13n}{n-1}=\dfrac{13n-13+13}{n-1}=\dfrac{13n-13}{n-1}+\dfrac{13}{n-1}=\dfrac{13\left(n-1\right)}{n-1}+\dfrac{13}{n-1}=13+\dfrac{13}{n-1}\)

\(\Rightarrow n-1\inƯ\left(13\right)=\left\{\pm1;\pm13\right\}\) \(\Rightarrow\left[{}\begin{matrix}n-1=1\\n-1=-1\\n-1=13\\n-1=-13\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}n=2\\n=0\\n=14\\n=-12\end{matrix}\right.\)