⁦Congruence in the integers⁩

⁦Every integer leaves 0, 1, 2 or 3 when divided by 4⁩. ⁦Numbers with the same remainder form a class⁩: ⁦1, 5, 9, 13 and so on all leave 1⁩.

⁦If a natural number m divides a - b we say a and b are congruent modulo m and write a≡b⁩. ⁦This means a and b leave the same remainder on division by m⁩. ⁦For example ١٧≡٢ mod 5 because ٥|١٧ − ٢⁩.

⁦You can add or subtract an integer on both sides of a congruence and multiply both sides by an integer⁩. ⁦So a big number can be replaced by its remainder⁩.

Uses: ⁦weekdays (mod 7), clock hours (mod 12) and check digits on numbers⁩.

⁦Work on the number chart or the answer box in each mission⁩.