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I am interested in the following set-up: Let $F \in \mathbb{Z}[x_1,\dots,x_n]$ be a fixed irreducible homogeneous polynomial of degree $d$ and consider the quantity $$N_{\delta}(B)=\#\{(x_1,\dots,x_n) ...

Take classic problem of finding $P,Q$ in balanced semi-prime $N=PQ$. $P$ has a binary expansion and so does $Q$. We can set the binary $0/1$ variables to be $x_1$ through $x_{\lceil\log P\rceil}$ and $...