# Automorphic Numbers with 5 Digits

## Theorem

The only $5$-digit automorphic number which does not begin with a zero is $90 \, 625$.

## Proof

We have:

$90 \, 625^2 = 8 \, 212 \, 8 \mathbf{90 \, 625}$

thus demonstrating it is automorphic.