Let $f(x)\in\mathbb Z[x]$ be a nonconstant polynomial, and let $$g(x,y)=\frac{f(x)-f(y)}{x-y}\in\mathbb Z[x,y].$$ Let $N(B)$ denote the number of pairs of integers $(x_0,y_0)$ such that $1\le x_0,y_0\le B$ and $g(x_0,y_0)=0$. Is it possible to obtain explicit asymptotics for $N(B)$ as $B\to\infty$?

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