Is it you who is defining the legitimacy here ? Let's not ask questions that would lead to proving something like x^n + y^n = z, only when n = 2. In order to show this is true you have to show it is not true for all n up to infinity. Quite a rabbit-hole and difficult. Has been done, but is this truly worth it in an interview ?

You should feel bad for being one of those who would end up dragging interview process to hell.