The (very nice) final problem of IMO 2017 asked contestants to show:

If $S$ is a finite set of lattice points $(x,y)$ with $\gcd(x,y)=1$, then there is a nonconstant homogeneous polyonmial $f \in \mathbb Z[x,y]$ such that $f(x,y) = 1$ for all $(x,y) \in S$.

It's claimed in this forum post that the above IMO problem is a special case of Lemma 7.3 of arXiv:1604.01704. The former post phrases the lemma as follows:

If $X$ is a finite scheme over $\operatorname{Spec} \mathbb Z$ then $\operatorname{Pic}(X)$ is finite.

Being unknowledgable as I am, I do not see how to deduce the IMO problem from the lemma. Can someone make the connection explicit?