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Is there an infinite sequence $a_1<a_2<\cdots $ such that $a_{i+1}-a_i=O(1)$ and no finite sum of $\frac{1}{a_i}$ is equal to $1$?
#299
:
[ErGr80]
number theory
,
unit fractions
There does not exist such a sequence, which follows from the positive solution to
[298]
by Bloom
[Bl21]
.
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