The discussion centers on proving the equivalence between the congruence classes and modular arithmetic, specifically the statement that [a][x_0] = [c] if and only if ax_0 ≡ c (mod m). Participants clarify that this stems from the definition of congruence classes, where [x] = [y] if x ≡ y (mod m). The proof involves demonstrating that [a][x_0] simplifies to [ax_0]. The justification of this relationship relies on the properties of transitivity and symmetry in congruence. Overall, the explanation successfully convinces participants of the theorem's validity.
