Gọi \(d=ƯCLN\left(2n+1;n+1\right)\left(d\in N\right)\)
\(\Leftrightarrow\hept{\begin{cases}2n+1⋮d\\n+1⋮d\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2n+1⋮d\\2n+2⋮d\end{cases}}\)
\(\Leftrightarrow1⋮d\)
\(\LeftrightarrowƯCLN\left(2n+1;n+1\right)=1\)
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