Solve the congruence 7x 4 mod 11 List three integers the con

Solve the congruence 7x 4 mod 11. List three integers the congruence.

Solution

# a b mod m if m | a-b #

7x 4 mod 11 if 11 | 7x - 4

which means 7x - 4 = 11 k .................(*)

x = (11 k + 4) / 7

therefore, k = 6,13,20,....

putting values of k in (*),we get

x = 10

x = 21

x = 32

x = 10 , 21 , 32 , 43,.....