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Does every finite colouring of the integers have a monochromatic solution to $1=\sum \frac{1}{n_i}$ with $2\leq n_1<\cdots <n_k$?
#46
:
[ErGr80]
[Er95]
[Er97c]
number theory
,
unit fractions
,
ramsey theory
The answer is yes, as proved by Croot
[Cr03]
.
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