Gọi \(d=ƯCLN\left(8n+10;6n+7\right)\left(d\in N\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}8n+10⋮d\\6n+7⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}24n+30⋮d\\24n+28⋮d\end{matrix}\right.\)
\(\Leftrightarrow2⋮d\)
Vì \(d\in N;2⋮d\Leftrightarrow d\in\left\{1;2\right\}\)
+) \(d=2\Leftrightarrow6n+7⋮2\)
Mà \(6n⋮2\)
\(\Leftrightarrow7⋮2\left(loại\right)\)
\(\Leftrightarrow d=1\)
\(\LeftrightarrowƯCLN\left(8n+10;6n+7\right)=1\left(đpcm\right)\)
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