MathDB
Shortlist 2017/N6

Source:

July 10, 2018
number theoryIMO ShortlistVieta Jumping

Problem Statement

Find the smallest positive integer nn or show no such nn exists, with the following property: there are infinitely many distinct nn-tuples of positive rational numbers (a1,a2,…,an)(a_1, a_2, \ldots, a_n) such that both a_1+a_2+\dots +a_n   \text{and}   \frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_n} are integers.
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