Question 6
An *irreducible lattice point* is an ordered pair of integers $(x,y)$ satisfying $\gcd(x,y) = 1$. Prove that if $S$ is a finite set of irreducible lattice points then there exists a nonconstant *homogeneous* polynomial $f(x,y)$ with integer coefficients such that $f(x,y)=1$ for each $(x,y) \in S$.