You all figured it out. Congratulations! I was actually hoping someone would give a different answer than quoting Wiles and Taylor's theorem. Notice that the points on the ellipse that intersect the rays generate a subfield of the complex numbers if their product equals one. And if a and b are rational, only two if n is odd (or four if n is even) of the points on the ellipse have rational coordinates. Is it possible to use this fact to generate a contradiction and prove FLT?