automorphic number

Given a base $b$ integer

 $n=\sum_{i=1}^{k}d_{i}b^{i-1}$

where $d_{1}$ is the least significant digit and $d_{k}$ is the most significant, if it’s also the case that the $k$ least significant digits of $mn^{2}$ are the same of those of $n$, then $n$ is called an automorphic number, or an $m$-automorphic number.

Neither $b$ nor $b+1$ can be 1-automorphic in base $b$.

Title automorphic number AutomorphicNumber 2013-03-22 16:20:17 2013-03-22 16:20:17 CompositeFan (12809) CompositeFan (12809) 5 CompositeFan (12809) Definition msc 11A63