2017 IMO Problems/Problem 6
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:
![\[a_0x^n + a_1x^{n-1} y + a_2x^{n-2}y^2 + \cdots + a_{n-1}xy^{n-1} + a_ny^n = 1.\]](http://latex.artofproblemsolving.com/c/3/3/c33a8093712f7fef24e6545476a95c7877da7250.png)
