How to isolate $A$ in $A\%B=C$

Question

How do I solve for a in the equation: $a\mod b= c\text{ (same as }a\%b=c$)

Is there an inverse mod, so that I can put the equation in terms of a?

Thanks in advance!

b and c can be any real number

I know that $a \mod b =a-\lfloor a/b\rfloor\cdot b$, so I can say $a = c+kb$ (k being any whole number), but I was woundering if there is an easier way to write this.

Answer 1

it means there exists $m \in \mathbb{Z}$ such that $a= bm+c$.

$a$ is not unique, for example if $b=2$ and $c=1$, then $a$ is the set of odd integers.