Divisibility

Aside

The notation is somewhat rare, and is commonly used in mathematical schools from the former Soviet Union. It is equivalent to .

Definition (divisibility)

Let , . Then is divisible by , or is divided by if

We will often call a divisor or factor of and a multiple of .

Examples

1. and since .
2. and since .

Question

• Does there exist a number such that it is divisible by all natural numbers?
• Does there exist a number such that it is divisible by all integer numbers?
• Does there exist a number such that it is divided by all integer numbers?

Divisibility by occurs often in mathematics, and, for this reason, has a dedicated name.

Definition (parity)

A number that is divisible by is called even. A number that is not divisible by is called odd. The property of a number to be even or odd is called parity.