Quite some time ago I saw an article where a Monte-Carlo algorithm for computing the Smith normal form of an integer matrix was described. In this article the following problem was posed:

Suppose $P, Q\in\mathbb{Z}[X,Y]$ are polynomials without a common factor. Then $(P(n,m), Q(n,m))$ has a density, i.e. there exist real numbers $\delta_k$, such that $$ \lim_{N\rightarrow\infty} \frac{1}{4N^2}\#\big\{(n,m):-N\leq n,m\leq N, (P(n,m), Q(n,m)) = k\big\} = \delta_k, $$ and $\sum_k\delta_k = 1$.

Can someone please give me a reference to this paper?