Definition:Proper Divisor/Integer

Definition
Let $\struct {\Z, +, \times}$ be the ring of integers.

Let $x, y \in \Z$.

Then $x$ divides $y$ is defined as:
 * $x \divides y \iff \exists t \in \Z: y = t \times x$

Then $x$ is a proper divisor of $y$ :


 * $(1): \quad x \divides y$
 * $(2): \quad \size x \ne \size y$
 * $(3): \quad x \ne \pm 1$

That is:
 * $(1): \quad x$ is a divisor of $y$
 * $(2): \quad x$ and $y$ are not equal in absolute value
 * $(3): \quad x$ is not equal to either $1$ or $-1$.

Also known as
A proper divisor is also known as a proper factor.

Also see

 * Definition:Aliquot Part


 * Definition:Aliquant Part