An ordered pair of integers is a primitive point if the greatest common divisor of and is . Given a finite set of primitive points, prove that there exist a positive integer and integers such that, for each in , we have:
An ordered pair $(x, y)$ of integers 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 exist a positive integer $n$ and integers $a_0, a_1, \ldots , a_n$ such that, for each $(x, y)$ in $S$, we have:
$$a_0x^n + a_1x^{n-1} y + a_2x^{n-2}y^2 + \cdots + a_{n-1}xy^{n-1} + a_ny^n = 1.$$
Školjka 
of integers is a primitive point if the greatest common divisor of 
and 
is 
. Given a finite set 
of primitive points, prove that there exist a positive integer 
and integers 
such that, for each 