# Explain example in Elkies's ABC Conjecture paper

The reference: The ABC's of Number Theory (PDF)

On page 17 of the PDF, or 72 of the scan, he solves a Putnam problem.

In the solution he uses a special case of Mason's theorem, for $F$ a polynomial, and gets the inequality:

$\text{deg}(P') = m-1 \geq 2m -r-s$

Can you explain how to derive this from the statement of Mason's theorem above, and specifically some intuition on what is $F^{-1}(\{0,1,\infty\})$, in relation to $F$ and how it counts roots, discarding multiplicity?

• Also, on page 16 of the PDF he writes: "more succinctly, $V_{D}(A)$ is the number of solutions to $F(t) = 0$ in $CP^1$. can you explain why? – Mariah Nov 18 '16 at 11:13