Problem #PRU-100244

Problem

Numbers 1 and 2 are written on a whiteboard. Every day Louise’s friend Zara changes these numbers to their arithmetic mean $a_m$ and harmonic mean $h_m$.

(The arithmetic mean of two numbers $a$ and $b$ is $a_m=\frac{a+b}{2}$, and harmonic mean of two numbers $a$ and $b$ is $h_m=\frac{2}{\frac{1}{a}+\frac{1}{b}}$ ).

(a) At some point Zara wrote $\frac{941664}{665857}$ as one of the two numbers (it is not known which). What was the other number written on the whiteboard at that time?

(b) Can $\frac{35}{24}$ be ever written by Zara on the whiteboard?