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Let $k\geq 2$ and $n$ be sufficiently large depending on $k$. Let $A=\{a_1<a_2<\cdots \}$ be the set of those integers in $[n,n^k]$ which have a divisor in $(n,2n)$. Estimate \[\max_{i} a_{i+1}-a_i.\] Is this $\leq (\log n)^{O(1)}$?
#693
:
[Er79e]
number theory
,
divisors
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[446]
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