# Modding the Digits

Call a number $$k$$ AP'ED if it is of the form $$k=a^b$$ with $$a$$ and $$b$$ integers such that $$a,b\ge2$$, $$a\leq9,$$ and the representation of $$k$$ is $$\overline{N_1N_2N_3\ldots}$$ where $$N_1\text{ mod } a\equiv N_2\text{ mod } a\equiv N_3\text{ mod } a\equiv\ldots\neq0.$$

Find the smallest AP'ED number.

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