Having a little trouble... I need to solve for x in the following congruence
8·x^13 ≡ 1 mod 17
By Fermat's theorem, $\displaystyle x^{16}\equiv1\!\!\!\pmod{17}$. So multiply both sides of your congruence by x^3 and you get $\displaystyle x^3\equiv8\!\!\!\pmod{17}$, which you should be able to solve just by looking at it.