# Left-Truncated Automorphic Number is Automorphic

## Theorem

Let $n$ be an automorphic number, expressed in some conventional number base.

Let any number of digits be removed from the left-hand end of $n$.

Then what remains is also an automorphic number.

## Examples

### Left-Truncation of $1 \, 787 \, 109 \, 376$

We have that $1 \, 787 \, 109 \, 376$ is automorphic:

$1 \, 787 \, 109 \, 376^2 = 3 \, 193 \, 759 \, 92 \, \mathbf {1 \, 787 \, 109 \, 376}$

Hence so is $109 \, 376$:

$109 \, 376^2 = 11 \, 963 \, \mathbf {109 \, 376}$