I'm currently taking Calculus I, so I'm new with mathematical notation. I always thought $x \bmod 3$ means the remainder when you divide $x$ by $3$. Am I wrong in thinking this is the remainder?
What is the difference between $x \pmod y$ and $\quad x \bmod y \quad$ in that sense?
Best Answer
In my experience, the expression $x\bmod y$ is a binary operation which returns the remainder when you divide $y$ into $x$.
By contrast, the parenthesized $\pmod y$ is used to qualify an equivalence. Thus one might write "$x_1\equiv x_2 \pmod y$". Usually the parenthesized $\pmod y$ goes at the right of the line, right-justified. So it is a qualifier which tells you which equivalence relation is intended. Therefore I think they have a different meaning.