Đặt ƯCLN(2n+5,3n+7) = d
Ta có: \(\hept{\begin{cases}2n+5⋮d\\3n+7⋮d\end{cases}\Rightarrow\hept{\begin{cases}3\left(2n+5\right)⋮d\\2\left(3n+7\right)⋮d\end{cases}\Rightarrow}\hept{\begin{cases}6n+15⋮d\\6n+14⋮d\end{cases}}}\)
\(\Rightarrow\left(6n+15\right)-\left(6n+14\right)⋮d\)
\(\Rightarrow6n+15-6n-14⋮d\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
\(\Rightarrow UCLN\left(2n+5,3n+7\right)=1\)
\(\Rightarrowđpcm\)
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