I used instead, and I reached the conclusion that are all divisible by . I know this in turn means the fractions assumed to be solutions are irreducible but I don't know how to prove that exactly.
Prove that the equation has no rational solutions.
I tried to go about this using the fact that for any integer , or , but when I supposed that there existed a rational solution and arrived to the equation , I can't draw the conclusion I want. How do I go about this? Any help would be appreciated.