I have an assignment, and two of the questions are bugging me.
Show that in the equation $$x^n + y^n =z^n$$ have a (non-trivial) whole number solution, so $$x^n + y^n =z^n \pmod p$$ for a prime number $p$, but not the other way around.
Show that Fermat's last theorem can be shown by $$x^4 + y^4 =z^4$$ and $$x^p + y^p =z^p $$ where $p$ is a odd prime.
I really need some help. Thanks.
From a lost senior year highschool student.