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Let $\\psi~\\mathbb{N} \\mapsto \\mathbb{R}$ be a non-negative function, and set $\\mathcal{E}_n :=\\bigcup \\left( \\frac{a - \\psi(n)}{n},\\frac{a+\\psi(n)}{n} \\right)$, where the union is taken over all $a \\in \\{1, \\dots, n\\}$ which are co-prime to $n$. Then the conjecture asserts that almost all $x \\in [0,1]$ are contained in infinitely many sets $\\mathcal{E}_n$, provided that the series of the measures of $\\mathcal{E}_n$ is divergent. 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