Modular arithmetic system of equations.

Question

I am trying to solve a system as follows... The $E_i$ are known and the $n_i$ are known. I need to solve for a unique $x$ that I know exists.

$$ E_1 \cong x mod n_1$$

$$ E_2 \cong x mod n_2$$

$$ E_3 \cong x mod n_3$$

$$ E_4 \cong x mod n_4$$

$$ E_5 \cong x mod n_5$$

I am not sure what I need to do... Thanks for the help.

Answer 1

The Chinese Remainder Theorem can solve this kind of system. Proof and how to use CRT One can also use the sage command CRT.