\(\Leftrightarrow3\left(2n+3\right)⋮3n+1\)
\(\Leftrightarrow6n+9⋮3n+1\)
\(\Leftrightarrow6n+2+7⋮3n+1\)
\(\Leftrightarrow3n+1\in\left\{1;7\right\}\)
mà n là số tự nhiên
nên \(n\in\left\{0;2\right\}\)
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\(\left(2n+3\right)⋮\left(3n+1\right)\)
\(\Rightarrow3\left(2n+3\right)⋮\left(3n+1\right)\)
\(\Rightarrow\left(6n+9\right)⋮\left(3n+1\right)\)
\(\Rightarrow\left(6n+2+7\right)⋮\left(3n+1\right)\)
\(\Rightarrow7⋮\left(3n+1\right)\)
\(\Rightarrow\left(3n+1\right)\inƯ\left(7\right)=\left\{1;-1;7;-7\right\}\)
\(\Rightarrow n\in\left\{0;-\dfrac{2}{3};2;-\dfrac{8}{3}\right\}\)
Mà \(n\in N\)
\(\Rightarrow n\in\left\{0;2\right\}\)
Vậy \(n\in\left\{0;2\right\}\) thì \(\left(2n+3\right)⋮\left(3n+1\right)\)
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