<s>[INST] solve the equation in Z Solve the equation over $\textbf{Z}$ : 
2$x^2$ - 2$xy$ - 5$x$ - $y$ + 19 = 0
I tried to obtain some $(A+B)^2$ terms, but I didn't make it. 
Thanks for your time!
 [/INST] $2x^2 - 2xy - 5x - y + 19 = 0 \to y = \dfrac{2x^2 - 5x + 19}{2x + 1} = x - 3 + \dfrac{22}{2x + 1}$. So $2x + 1 | 22$, and $2x + 1 = 1, -1 , 11, -11$. we can then find $y$ for each value of $x$ listed.
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