1. $\displaystyle (\phi_a) : $$\displaystyle \mathbb{Z}_5 $ [x] $\displaystyle \ \rightarrow \ (\mathbb{Z}_5) $ be an evaluation homonophism. Use Fermat's Theorem to evaluate $\displaystyle \phi_3(x^{231} + 3x^{117} - 2x^{53} +1) $.
2. Use Fermat's Theorem to final all zeros in
$\displaystyle \mathbb{Z}_5 $ of $\displaystyle 2x^{219} + 3x^{74} + 2x^{57} + 3x^{44}. $

thanks !