Question

Tìm tất cả các số tự nhiên n để 2n+5 chia hết cho n+1

Answer 1

\(2n+5⋮n+1\)

Mà \(n+1⋮n+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}2n+5⋮n+1\\2n+2⋮n+1\end{matrix}\right.\)

\(\Leftrightarrow3⋮n+1\)

\(\Leftrightarrow n-1\inƯ\left(3\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}n+1=1\\n+1=3\\n+1=-1\\n+1=-3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=0\\n=2\\n=-2\\n=-4\end{matrix}\right.\)

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