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Prove that the number $1$ can be written as a sum of $2023$ fractions

Source: Moldova EGMO TST 2023

February 4, 2023
combinatorics

Problem Statement

Prove that the number 11 can be written as a sum of 20232023 fractions of the form 1ki\frac{1}{k_i}, where all nonnegative integers ki(1≤i≤2023)k_i (1\leq i\leq 2023) are distinct.
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