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Take a bivariate polynomial of total degree $d$ satisfying $d=d_x=d_y>1$ in $\mathbb Z[x,y]$ with coefficients bound in absolute value by $b$ ($d_x$ is $x$-degree and $d_y$ is $y$-degree). Given a ...

Take a bivariate polynomial of degree $d_x+d_y>\max(d_x,d_y)>1$ in $\mathbb Z[x,y]$ with coefficients bound in absolute value by $b$ ($d_x$ is $x$-degree and $d_y$ is $y$-degree). What is the ...