As part of a proof of the CRT, I've encountered the following:
We want to find a solution for the system
$$x \equiv a_1 \pmod{n_1} \\ x \equiv a_2 \pmod{n_2}$$
Then the author look for a solution of the form $x= a_1 +dy$ and claims that the system is equivalent to:
$$dy \equiv 0 \pmod{n_1} \\ dy \equiv a_2 - a_1 \pmod{n_2}$$
In the second equation it seems like he was able to "move" the $a_1$ term to the other side of the equivalence - Why is it valid?
\pmod
to write $\mod{}$ in brackets. – Math Lover Dec 01 '17 at 22:30