\(n+3\) \(và\) \(3n+8\)
\(Gọi\) \(ƯCLN\left(n+3,3n+8\right)=d\)
\(Ta\) \(có\):
\(\hept{\begin{cases}n+3\\3n+8\end{cases}\Rightarrow\hept{\begin{cases}3\left(n+3\right)⋮d\\3n+8⋮d\end{cases}}\Rightarrow\hept{\begin{cases}3n+9⋮d\\3n+8⋮d\end{cases}}}\)
\(\Rightarrow\left(3n+9\right)-\left(3n+8\right)⋮d\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
\(Mà\) \(ƯCLN\left(n+3,3n+8\right)=1\)
\(\Rightarrow n+3,3n+8\) \(là\) \(hai\) \(số\) \(nguyên\) \(tố\) \(cùng\) \(nhau\)