Question

Tìm số nguyên n sao cho :

(2n-5)chia hết cho n

Answer 1

Vì 2n - 5 \(⋮\) n mà 2n \(⋮\) n nên :
=> 5 \(⋮\) n hay n \(\in\) Ư(5)
Ư(5) = {\(\pm\)1;\(\pm\)5}
n \(\in\) {\(\pm\)1;\(\pm\)5}
Vậy n \(\in\) {\(\pm\)1;\(\pm\)5}

Answer 2

\(\left(2n-5\right)⋮n\)

\(\Rightarrow n+n-5⋮n\)

Vì \(n+n⋮n\) nên \(-5⋮n\)

\(\Leftrightarrow2n-5\inƯ\left(-5\right)=\left\{-5;-1;1;5\right\}\)

\(2n-5\)	\(-5\)	\(-1\)	\(1\)	\(5\)
\(n\)	\(0\)	\(2\)	\(3\)	\(5\)

Vậy \(2n-5\in\left\{0;2;3;5\right\}\)