Question

Tìm n thuộc Z, biết

\(\frac{3}{n-2}\)thuộc Z

\(\frac{n}{n-1}\)thuộc Z

Answer 1

Ta có :
\(\frac{3}{n-2}\in Z\)

\(\Rightarrow n-2\inƯ\left(3\right)\)

\(Ư\left(3\right)=\){\(-3;-1;1;3\)}

Nếu x - 2 = -3 \(\Rightarrow\)x = -1.Nếu x  -2 = -1 \(\Rightarrow\)x = 1.Nếu x - 2 = 1 \(\Rightarrow\)x = 3Nếu x - 2 = 3 \(\Rightarrow\)x = 5.

\(\Rightarrow x\in\){ \(-1;1;3;5\)}

b, Để \(\frac{n}{n-1}\in Z\)

\(\Rightarrow\)\(n-1\ne0+1\Leftrightarrow n\ne1\)

\(\Rightarrow n-1\inƯ\left(n\right)\)...