I have a congruence system to solve, that I actually tried to solve. The problem is that I'm not sure that I did it right, because at the end I cannot find a proper number that will be working fine for all of the equations.
At the end I have a equation like:
$x=7k+6 = 7(13y+1)+6 = 91y+13 = 455z-806 = 455(11b+813/455) = 11b + 7$
So at the end there is this nice reduction of 455. I thought it was a good sign that I did everything properly. Neverthless, whichever $b$ I can think of, the answer is not right for all of the congruences above. I tried $n = 0, 1, 2, 3, ... 10 (x=7, 18, 19, 29, 40, 51 ...)$ and I cannot find a proper answer. How to easily deal with such tasks?
Thank you for any advices!