\(x\)\(=\)-2016
\(\dfrac{8n+193}{4n+3}\)=\(\dfrac{2\left(4n+3\right)+187}{4n+3}\)=2+\(\dfrac{187}{4n+3}\)
Để \(\dfrac{8n+193}{4n+3}\)là số nguyên thì 4n+3 thuộc Ư(187)
Ư(187)=(1;-1;11;-11;17;-17;187;-187)
ta có :
4n+3 | 1 | -1 | 11 | -11 | 17 | -17 | 187 | -187 |
n | -1 | \(\dfrac{1}{2}\) | 2 | \(\dfrac{-7}{2}\) | \(\dfrac{7}{2}\) | -5 | 46 | \(\dfrac{-95}{2}\) |
Vậy n =(-1;2;-5;46)