[SOLVED] Find All Solutions of the Congruence Hi, I am having lots of trouble understand how to do the following question: Find all solutions of 8x congruent to 6 mod 14. I know that the GCD is 2. Therefore there should be two equivalence classes of solutions. But what is the PROPER way to find them? I know that they are  and . But I only can seem to get . That being said I don't think the process in which I get  is the right way to do it either. How do I find ? I have spend LONG hours looking over my notes, reading the text, trying to understand the theory behind congruence classes. But I still don't understand how I can find all the equivalence classes of solutions. I always just get one. Even though I know there is more than one. What is the PROPER way to find all classes? For example, I use the euclidean algor. to get GCD of 2. Then I do the following 2 = 8 - 1*6 2 = 8 - 1*(14 - 1*8) 2 = 8 - 1*14 + 1*8 2 = 2*8 - 1*14. I then multiply 2 = 2*8 - 1*14 by 3 and get 6 = 6*8 - 6*14. From the term 6*8 I get the equivalence class of . First of all, am I proceeding in the correct way for finding the equivalence class of ? Secondly, how do I find the equivalence class of ? Any help is appreciated. Thankyou.