Good evening, I'm reading Lamé's proposed proof for Fermat's last theorem. He get to this equation: $$x^n+y^n=(x+y)(x+jy)(x+j^2y)\cdots(x+j^{n-1}y)$$ where $j$ is the n-th root of unity. Then he proof that each of the $x+j^iy$ is relatively prime to the others, so that it is an nth power.
Finally the book says that Lamé closed his proof showing how this condition leads to infinite descent, but I'm not able to see how...
Could anyone help me, please?
