Find three integer solutions to the equation 5x 4mod 3 Can y

Find three integer solutions to the equation 5x 4(mod 3). Can you find a formula for all integer solutions?

Solution

5x=4 mod 3

5=6-1

(6-1)x=4 mod 3

6x-x=3+1 mod 3

-x=1 mod 3

x=-1 mod 3

x=3m-1 , where m is any integer

This is formula for all integer solutions

Seting , m=0,1,2 we get three solutions

x=-1,2,5