Gọi d là ƯCLN(2n+1;n+1) ( d\(\inℕ^∗\))
\(\Rightarrow\hept{\begin{cases}2n+1⋮d\\n+1⋮d\end{cases}}\Rightarrow\hept{\begin{cases}2n+1⋮d\\2\left(n+1\right)⋮d\end{cases}\Rightarrow\hept{\begin{cases}2n+1⋮d\\2n+2⋮d\end{cases}}}\)
\(\Rightarrow\left(2n+2\right)-\left(2n+1\right)⋮d\)
\(\Rightarrow1⋮d\)
Mà d \(\inℕ^∗\Rightarrow d=1\)
Hay 2n+1;n+1 nguyên tố cùng nhau