Write \frac{1}{\sqrt[5]{2}-1}=a+b \sqrt[5]{2}+c \sqrt[5]{4}+d \sqrt[5]{8}+e \sqrt[5]{16}, with a, b, c, d, and e integral. Find a^{2}+b^{2}+ c^{2}+d^{2}+e^{2}.
Write \frac{1}{\sqrt[5]{2}-1}=a+b \sqrt[5]{2}+c \sqrt[5]{4}+d \sqrt[5]{8}+e \sqrt[5]{16}, with a, b, c, d, and e integral. Find a^{2}+b^{2}+ c^{2}+d^{2}+e^{2}.