Gọi \(d=ƯCLN\left(2n+3;n+1\right)\)
\(\Leftrightarrow\hept{\begin{cases}2n+3⋮d\\n+1⋮d\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2n+3⋮d\\2n+2⋮d\end{cases}}\)
\(\Leftrightarrow1⋮d\)
Vì \(d\in N\)*; \(1⋮d\Leftrightarrow d=1\)
\(\LeftrightarrowƯCLN\left(2n+3;n+1\right)=1\)