I'm having trouble following one step in the proof of Liouville's theorem on approximation of real algebraic numbers, from Murty and Rath's book "Transcendental Numbers".
The step is:
I'm happy to provide more context, but I suspect it won't be neccesary. Feel free to ask for a sketch of the rest of the proof.
The notation is:
$\alpha$ is the real algebraic number of degree $>1$ we are trying to approximate.
$p/q$ is any rational number with $(p,q)=1$, $q>0$.
$\alpha_2,...,\alpha_n$ are the other roots of the minimal polynomial of $\alpha$.