# Left-Truncated Automorphic Number is Automorphic

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## 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.

## Proof

## 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 $109 \, 376$:

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

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $1,787,109,376$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $1,787,109,376$