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 \(h_m = \frac{2}{\tfrac{1}{a} + \tfrac{1}{b}}\) ).
(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?