MathDB

Let

N=\overline{abcd}

be a positive integer with four digits. We name plátano power to the smallest positive integer

p(N)=\overline{\alpha_1\alpha_2\ldots\alpha_k}

that can be inserted between the numbers

\overline{ab}

and

\overline{cd}

in such a way the new number

\overline{ab\alpha_1\alpha_2\ldots\alpha_kcd}

is divisible by

N

. Determine the value of

p(2025)

1