Gọi ƯCLN(3n+5,8n+13) là d (d\(\in\)Z*)
\(\Rightarrow\hept{\begin{cases}3n+5\\8n+13\end{cases}}\)\(⋮\)d \(\Rightarrow\hept{\begin{cases}13\left(3n+5\right)\\5\left(8n+13\right)\end{cases}}\)\(⋮\)d
\(\Rightarrow\hept{\begin{cases}39n+65\\40n+65\end{cases}}\)\(⋮\)d
\(\Rightarrow\)-1\(⋮\)d
\(\Rightarrow\)1\(⋮\)d
\(\Rightarrow\)d=1
\(\Rightarrow\)đpcm