divisibility

Given integers $a$ and $b$ , then we say $a$ divides $b$ if and only if there is some $q \in \mathbb{Z}$ such that $b=qa$ .

There are many other ways in common use to express this relationship:

• $a\mid b$ (read ``$a$ divides $b$ '').
• $b$ is divisible by $a$ .
• $a$ is a factor of $b$ .
• $a$ is a divisor of $b$ .
• $b$ is a multiple of $a$ .

The notion of divisibility can apply to other rings (e.g., polynomials).