I got two questions that im wondering, one main question and one "bonus" question I guess
1) what is the general method to solve congruence equations like ax ≡ b (mod m) ?
take for example 3x≡2 (mod 5) how would I go about solving this?
I was able to solve it using trial and error and found the answer to be 4, but Im looking for a better and faster way to solve problems like these for larger m 's..
also im wondering sometimes you can solve these with just the inverse of a, but when does that apply? only when b=1 and a and m are coprime? example 9x≡1 (mod 14) for instance?
2) can someone please show me how I can find the modular inverse of 9 in mod14 ?, im familiar with the method used and Im able to find the inverse in other examples, but im not sure why this one is casuing me so much trouble, answer should be 11 I think