a) Gọi ƯCLN\(\left(n+2;n+3\right)\)=d
\(\Rightarrow\left\{{}\begin{matrix}\left(n+3\right)⋮d\\\left(n+2\right)⋮d\end{matrix}\right.\)\(\Rightarrow\left(n+3-n-2\right)⋮d\Leftrightarrow1⋮d\Leftrightarrow d=1\)
\(\Rightarrow\)ƯCLN\(\left(n+2;n+3\right)\)=1 \(\forall n\in N\)
b) Gọi ƯCLN\(\left(2n+1;9n+4\right)\)=d
\(\Rightarrow\left\{{}\begin{matrix}\left(2n+1\right)⋮d\\\left(9n+4\right)⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}9\left(2n+1\right)⋮d\\2\left(9n+4\right)⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(18n+9\right)⋮d\\\left(18n+8\right)⋮d\end{matrix}\right.\)\(\Rightarrow\left(18n+9-18n-8\right)⋮d\)
\(\Leftrightarrow1⋮d\Leftrightarrow d=1\)
\(\Rightarrow\)ƯCLN\(\left(2n+1;9n+4\right)\)=1 \(\forall n\in N\)
