Question

Tìm n \(\in\) N sao cho (3n+2) \(\vdots\) (n -1)

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Answer 1

\(\left(3n+2\right)⋮\left(n-1\right)\)

\(\Rightarrow\left(3n-3+5\right)⋮\left(n-1\right)\)

\(\Rightarrow5⋮\left(n-1\right)\)

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

\(\Rightarrow n\in\left\{-4;0;2;6\right\}\)

Answer 2

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Answer 3

\(3n+2⋮n-1\)

\(\Rightarrow3\left(n-1\right)+5⋮n-1\)

\(\Rightarrow5⋮n-1\)

\(\Rightarrow n-1\inƯ\left(5\right)=\left\{5,-1,-5,1\right\}\)

\(\Rightarrow n\in\left\{6,0,2,-4\right\}\)

\(\Rightarrow n\in\left\{0,2,6\right\}\)