â) Gọi \(d=ƯCLN\left(4n-13;5n-16\right)\left(d\in N\right)\)

\(\Leftrightarrow\left\{{}\begin{matrix}4n-13⋮d\\5n-16⋮d\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}20n-65⋮d\\20n-64⋮d\end{matrix}\right.\)

\(\Leftrightarrow1⋮d\)

Vì \(d\in N;1⋮d\Leftrightarrow d=1\)

\(\LeftrightarrowƯCLN\left(4n-13;5n-16\right)=1\)

\(\Leftrightarrow\) Phân số \(\dfrac{4n-13}{5n-16}\) tối giản với mọi n

b) Gọi \(d=ƯCLN\left(5n-13;3n-8\right)\)

\(\Leftrightarrow\left\{{}\begin{matrix}5n-13⋮d\\3n-8⋮d\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}15n-39⋮d\\15n-40⋮d\end{matrix}\right.\)

\(\Leftrightarrow1⋮d\)

Vì \(d\in N;1⋮d\Leftrightarrow d=1\)

\(\LeftrightarrowƯCLN\left(5n-13;3n-8\right)=1\)

\(\Leftrightarrow\) Phân số \(\dfrac{5n-13}{3n-8}\) tối giản với mọi n