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# Kaprekar numbers

Please do not rely on any information it contains.

A number ${\displaystyle n}$ is a Kaprekar number in a given base ${\displaystyle b}$ if the base ${\displaystyle b}$ digits of ${\displaystyle n^{2}}$ can be split into two numbers ${\displaystyle \alpha }$ and ${\displaystyle \delta }$ such that ${\displaystyle \alpha +\delta =n}$.
Preferably ${\displaystyle \alpha }$ and ${\displaystyle \delta }$ have the same number of digits, but this is not required and in some cases not possible (when ${\displaystyle \lfloor \log _{b}n^{2}\rfloor }$ is odd). Furthermore, ${\displaystyle \delta }$ may have padding zeroes that become inconsequential when computing ${\displaystyle \alpha +\delta }$.