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This is my question that I posted at "I want to find the numbers $a$, $b$, $c$, $d$ of the function $y = \dfrac{a x + b}{c x + d}$ so that the triangle $ABC$ with three points $A$, $B$, $C$ have integer coordinates and lies on the graph of the given function, then the centroid of the triangle $ABC$ (have also integer coordinates) is also lies on the graph". The anserw at that site is yes. But, he said "I think I was just lucky to get an integer solution since I haven't imposed all the constraints".

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My student found a function $y = \dfrac{93 x + 6}{x+2}$. Then, $A(-6,138)$, $B(8,75)$, $C(-62,96)$ and centroid $G(20,103)$.

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