Đặt U(n, 2n+1)=d
\(\Rightarrow\left\{{}\begin{matrix}n⋮d\\2n+1⋮d\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}2n⋮d\\2n+1⋮d\end{matrix}\right.\)\(\Rightarrow2n+1-2n⋮d\)\(\Rightarrow1⋮d\)
\(\Rightarrow d\in\left\{\pm1\right\}\)
Vậy \(\dfrac{n}{2n+1}\)tối giản