Image of Integer Square Function

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Theorem

The image of the integer square function is the set of square numbers.


Sequence of Square Numbers

The sequence of square numbers, for $n \in \Z_{\ge 0}$, begins:

$0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, \ldots$


Proof

Follows directly by definition of the integer square function.

$\blacksquare$