Answer the following using the group U12 a solve the equatio

Answer the following using the group U12

a) solve the equation 7x = 11

U12 is the group of units in Z12 which contains the elements

{1,5,7,11} basically all the integers modulo 12, coprime to 12 will have units in Z12

a)7x=11

7 is a unit and what is it\'s inverse? If we multiply both sides by inverse of 7 we can solve the problem

It has to be one of the 4 elements in U12

7*7=49=48+1=1 mod 12

So, 7 is the inverse

7x=11 mod 12

Multiply both sides by 7 gives

7^2x=77 mod 12

x=72+5 mod 12

x=5 mod 12