Let $n_{1} < n_{2} < \dots$ be an infinite sequence of integers with associated $a_{k} (mod n_{k})$ , such that for some $ϵ > 0$ we have $n_{k} > (1 + ϵ) k lo g k$ for all $k$ . Then $# {m < n_{k} : m \neq \equiv a_{i} (mod n_{i}) for 1 \leq i \leq k} \neq = o (k) .$

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number theory · solved · 0 attempts

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