| m \mid n | m divides n |
| m \nmid n | m does not divide n |
| n \equiv r (mod m) | m \mid (n-r), that is, as m divides n-r, n and r have the same remainder when divided by m |
| \lfloor x \rfloor | floor function: largest integer not larger than x |
| n mod m | (binary operator) remainder of n when divided by m (m is called the modulus, which we assume here to be a positive integer). Equal to n-m \lfloor \frac{n}{m} \rfloor. Note that 0 \le r \lt m. In C, Python, Java, and pari-gp, it can be computed using using the % binary operator (applied to unsigned integers). |
| gcd(a,b) | gratest common divisor of a and b. |
| lcm(a,b) | least common multiple of a and b; equal to ab/ gcd(a,b). |
| \mathbb{Z}_m | set of equivalence classes modulo m; slightly abusing the mathematical notation for equivalence classes, \mathbb{Z}_m = \lbrace 0, 1, ..., m-1 \rbrace. |
