Solve the Congruence 3x equiv 1 mod17 Use a to solve 3x equi

Solve the Congruence 3x equiv 1 (mod17) Use (a) to solve 3x equiv 5 (mod17)

Solution

a)

Note:3*6=18=17+1=1 mod 17

So we multiply this equation by 6 to get

18x=6 mod 17

18x=x=6 mod 17

So, solution is

x=6 mod 17

b)

We solved:

3y=1 mod 17 in part a)

MUltiplying by 5 gives

15y=5 mod 17

3(5y)=5 mod 17

We need to solve

3x=5 mod 17

So, x=5y mod 17

But, y=6 mod 17

So, x=5*6=30=13 mod 17

x=13 mod 17