Prove that $x$ is congruent to $y \pmod m$ if and only if $x = km + y$ Prove that $x$ is congruent to $y \pmod m$ if and only if $x = km + y$


I'm not sure how to prove this, and honestly I don't really understand why it's true in the first place.
If $x \equiv y \pmod m$, then after division of $x$ by $m$, I have a remainder of $y$, assuming $0 \leq y &lt; m$. So, via the division algorithm, $x = mq +y$. 
The other direction is trivial using the division algorithm.
If $x \equiv y \pmod m$, then after division of $x$ by $m$, I have a remainder of $y$, assuming $0 \leq y &lt; m$. So, via the division algorithm, $x = mq +y$. 
The other direction is trivial using the division algorithm.