Vì : \(3n+7⋮2n+1\)
\(\Rightarrow2\left(3n+7\right)⋮2n+1\)
\(\Rightarrow6n+14⋮2n+1\) (1)
Vì : \(2n+1⋮2n+1\)
\(\Rightarrow3\left(2n+1\right)⋮2n+1\)
\(\Rightarrow6n+3⋮2n+1\) (2)
Từ (1) và (2)
\(\Rightarrow\left(6n+14\right)-\left(6n+3\right)⋮2n+1\)
\(\Rightarrow6n+14-6n-3⋮2n+1\)
\(\Rightarrow11⋮2n+1\Rightarrow2n+1\inƯ\left(11\right)\)
\(Ư\left(11\right)=\left\{1;11\right\}\)
+) \(2n+1=1\Rightarrow2n=1-1\Rightarrow2n=0\Rightarrow n=0\)
+) \(2n+1=11\Rightarrow2n=11-1\Rightarrow2n=10\Rightarrow n=5\)
Vậy : \(n\in\left\{0;5\right\}\)
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