Prove that for any integer $n > 3$ there exist positive integers $a_1 > \dots > a_n$ such that $1 = \frac{1}{a_1} + \dots + \frac{1}{a_n}$
For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$