I'm trying to pack some integers into one using the Chinese Reminder Theorem. Taking the example below:
The integers that I want to pack are : {3,6,4}.
Using the theorem, we have :
$\chi \equiv 3 \mod {5}$
$\chi \equiv 6 \mod {7}$
$\chi \equiv 4 \mod {11}$
and, I found $\chi = 48$
Cloud you please let me know if there is a method to found the three number 3, 6, and 4 if we have just 48 and the list {5,7,11}?
$$48=5\cdot 9+3\\ 48=7\cdot 6+6\\ 48=11\cdot 4+4$$
The last part in each are the congruence classes used. That's how we would find the answer for such a small example.