I am really struggling with how to solve systems of congruences and I have a problem I need to solve as well as some attempt to solve it so any additional help would be so greatly appreciated!
Equations: x = 3 mod 4
x = 4 mod 5
x = 6 mod 7
I started by saying the solution will look like x = 7n + 6 and did the following:
7n+6 = 4mod5
7n = -2mod5
7n = 3mod5
2n = 3mod5
n = (3)(2)n = 3(3) = 9 = 4mod5
so then n = 5k + 4
plug it back in and x = 7(5k+4) +6 = 35k + 34
then plugging that one in to another equation you get
35k + 34 = 3mod4 and 3k = 1mod4
and at this point I just feel completely lost and don't know why I am doing the computations I am doing and where I want to get or anything for that matter.
Any guidance would be super appreciated!