Difficult# Solving Quadratic Congruence: $\mathbb{Z}_{29}$

NUMTH-DJAXBR

Denote by $\mathbb{Z}_{29}$ the set of all congruence classes modulo $29$. Consider the following quadratic congruence:

$$ x^2 + x + 1 \equiv 0 \ \mathrm{mod} \ 29 $$

Which of the following statements are correct? Select **ALL** that apply.