Question 154
Let $z = e^{\frac{2\pi i}{101}}$ and let $\omega = e^{\frac{2\pi i}{10}}$. Prove that
$$
\prod_{a=0}^{9} \prod_{b=0}^{100} \prod_{c=0}^{100} \left(\omega^{a} + z^{b} + z^{c}\right)
$$
is an integer and find (with proof) its remainder upon division by $101$.
$$
\prod_{a=0}^{9} \prod_{b=0}^{100} \prod_{c=0}^{100} \left(\omega^{a} + z^{b} + z^{c}\right)
$$
is an integer and find (with proof) its remainder upon division by $101$.