This thesis discusses some of the r characteristic that satisfy the equation 11x ≡ r (mod 100) and 111x ≡ r (mod 1000), where r € Ɲ and positive integer x ≥ 0. In general the r value obtained is x as tens and the units is 1. In the equation 11x ≡ r (mod 100) and 111x ≡ r (mod 1000), for x = 10m the value r = 1 and for the value x = 10m + 1 obtained value r = 11. The value obta…