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Mathematics > Combinatorics
Title: A question of Erdős and Graham on Egyptian fractions
(Submitted on 24 Apr 2024)
Abstract: Answering a question of Erd\H{o}s and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit constant $c_x$ increasing with $x$.
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