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Let $r(a,b)$ be a rational number depending on $a,b$ and nonnegative. For every $b$ there is an $a$ such that $r(a,b)$ is not $0$.
Let $C(a,b)$ be a squarefree positive integer depending on $b$ and different for every $b$.
Consider for positive integers $I,J$ :
$$ S_J = \sum_{j=1}^J \sum_{i=1}^I ...
