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 $m{n}^2$ 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 $b$.