this might be a (very) stupid question, however I need to ask it (why?). I have the congruence $84x ≡ 68$ $(mod$ $400)$ from: Congruence equation ..., where the solution is given.
However, I tried to solve this using the Chinese Remainder Theorem and got the wrong answer. So my question is, can I use CRT to solve this and if so please provide an answer, if I can't use CRT why not, what condition is not fullfilled?
Ok, I might not have been clear. When applying CRT I get:
Primefactorization of $400 = 2^4*5^2$ then:
$84x ≡ 68$ $(mod$ $2^4)$ ↔ $4x ≡ 4$ $(mod$ $2^4)$ ↔ $x ≡ 1$ $(mod$ $2^4)$ $(1)$
$84x ≡ 68$ $(mod$ $5^2)$ ↔ $9x ≡ 14$ $(mod$ $5^2)$ ↔ $x ≡ 21$ $(mod$ $5^2)$ $(2)$
From (1) and (2) I get: $x = 1 + 16s ≡ 21$ $(mod$ $25)$ → $s = 20 + 25*t$ → $x = 321 + 400t$ which is wrong :(
Where am I going wrong?
Regards