BdMO Online Forum

An ordered pair $(x,y)$ of integer is a primitive point if the greatest common divisor of $x$ and $y$ is $1$. Given a finite set $S$ of primitive points.Prove that there exists a positive integer $n$ and integers $a_0,a_1,...,a_n$ such that for each $(x,y)$ in $S$, we have

$a_0x^n+a_1x^{n-1}y + ...+ a_{n-1}xy^{n-1} +a_ny^n=1$