Find all solutions to the following linear congruences You m

Find all solutions to the following linear congruences. You may use either form (b) or (c) from the previous problem-whichever you prefer. But the form of your answer must match the form of the question. In Z7, or equivalently 3x 2 mod 7. in Z9, or equivalently 6x 3 mod 9. in Z1597, or equivalently 987x 610 mod 1597.

Solution

(a)     (3x-2 )/7 =k where k is an integer

       That is 3x-2 =7k   or 3x=7k+2

Here   k=1    gives x=3

K=4   gives   x=10

k=7    gives x=17

The solutions are { 3,10,17,24-----------------------------}

(b) (6x-3)/9=k

This means   6x-3=9k or   2x-1=3k

2x=3k+1

k=1 gives x=2

k=3 gives x=5

k=5 gives   x=8

Therefore the solution is {2,5,8..................................}