Find the smallest positive integer n or show no such n exists, with the following property: there are infinitely many distinct n-tuples of positive rational numbers (a1,a2,…,an) 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. number theoryIMO ShortlistVieta Jumping