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MathNet 2008-part-02 — 165 problems (EN–VI) Question 118

Math Olympiad Vault · MathNet 2008-part-02 — 165 problems (EN–VI)

Question 118

Does there exist a positive integer $n$ satisfying the following condition?

Condition: For an arbitrary rational number $r$, there exist an integer $b$ and nonzero integers $a_1, a_2, \dots, a_n$ such that
$$
r = b + \frac{1}{a_1} + \dots + \frac{1}{a_n}
$$