I have read in many places that the Frey curve (if it existed) $y^2=x(x-A)(x+B)$ (or equivalently, $y^2=x(x-A)(x-C)$ corresponds to the solutions of $a^n+b^n=c^n$, where $A=a^n/c^n$ and $B=b^n/c^n$.
However, the connection is not very clear to me. Can someone either explain it or point me to a source that would spell this out step by step?
Edit: Just to clarify, I am asking about the correspondence between the Frey curve and the solutions to Fermat's Last Theorem. I take it there is no simple relation between the two?