Question

Tim stn n de n+1 va n-3 la 2 snt cung nhau

Answer 1

\(Giai\)

\(Goi:d=\left(n+1,n-3\right).\)

\(taco:\hept{\begin{cases}n+1⋮d\\n-3⋮d\end{cases}}\Rightarrow\left(n+1\right)-\left(n-3\right)⋮d\Leftrightarrow4⋮d\Rightarrow d\in\left\{1;2;4\right\}\)

\(\left(n+1,n-3\right)=1\Leftrightarrow d=1\Leftrightarrow\orbr{\begin{cases}n+1=2k+1\left(k\inℕ\right)\\n-3=2k+1\left(k\inℕ\right)\end{cases}\Leftrightarrow\orbr{\begin{cases}n=2k\\n=2k+4\end{cases}}}\left(n,chẵn\right)\)

\(Vậy:với,n,chẵn,thì,:\left(n+1,n-3\right)=1\)