1 Express the solutions to the following linear congruences

1) Express the solutions to the following linear congruences in terms of unions of congruence classes. Use a multiplicative inverse to solve the linear congruence when applicable.

a) 6x 9 mod 15

b) 7x 2 mod 12

c) 3x 7 mod 12

Solution

a.

6X = 9 mod 15 then 6x 9 x15

6x 135

x 135/6 [By dividing on both the sides by 6]

x 22.5

b.

7x 2 mod 12

7x 2 x12

7x 24

x 24/7 [By dividing on both the sides by 7]

x 3.42

c.

3x 7 mod 12

3x 7 × 12

3x 84

x 84/3 [By dividing on both the sides by 3]

x 26