Definition:Square Number

Definition
An integer $n$ is defined as square number :
 * $\exists m \in \Z: n = m^2$

The sequence of square numbers, for $n \in \Z_{\ge 0}$ begins:
 * $0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, \ldots$

Also known as
A square number is often referred to as a square.

For emphasis, a square number is sometimes referred to as a perfect square, but this could cause confusion with the concept of perfect number, so its use is discouraged.

Also see

 * Odd Number Theorem for a well-known recurrence relation defining the square numbers.


 * Definition:Polygonal Number

Historical Note
The square numbers were classified and investigated by the Pythagorean school in the $6$th century BCE. This was possibly the first time this had ever been done.