Problem

Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade

Tags: number theory, algebra, combinatorics



Let $A_n$ be the number of arranged n-tuples of natural numbers $(a_1,a_2…a_n)$, such that $\frac{1}{a_1} +\frac{1}{a_2} +...+\frac{1}{a_n} =1$. Find the parity of $A_{68}$.