(Exercise 3.7 from the notes)

Under what condition on the digits $\mathrm{x}$ and $\mathrm{y}$ is the number $\overline{27 x 85 y}$ divisible by 33?

inverses modulo $n$

Definition 8 (inverse modulo $n$).

Proposition 9 (criterion for invertibility modulo $n$).

Proposition 10 (simplification modulo $n$).
$\mathrm{x}+\mathrm{y}$ congruent to 2 modulo 3 and $\mathrm{y}$-x congruent to 2 modulo 11