Find all six solutions to 12x = 24 mod 30 (= is congruence not equality...)
Book says to use this theorem:
Supposed divides a, c, m. Then every solution of
(a/d)x =(c/d) mod (m/d)
corresponds tod distinct solutions (modulo m) of
ax = c mod m:
Not sure how to show this because it seems to me that there would be infinite solutions. How do I do this?
The theorem the book asks you to use is the Linear Congruence Theorem which is used to solve linear congruences as yours
Note that as Drexel said, the values of x "wrap around" (x = 30 is equivalent to x = 0, x = 31 is equivalent to x = 1, ...). But the LCT basically provides a general formula that gives all solutions to your congruence, so you don't have to worry about whether there are infinite solutions, since the formula gives them all