Problem

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Tags: number theory



Determine all positive integers $A= \overline{a_n a_{n-1} \ldots a_1 a_0}$ such that not all of its digits are equal and no digit is $0$, and $A$ divides all numbers of the following form: $A_1 = \overline{a_0 a_n a_{n-1} \ldots a_2 a_1}, A_2 = \overline{a_1 a_0 a_{n} \ldots a_3 a_2}, \ldots ,$ $ A_{n-1} = \overline{a_{n-2} a_{n-3} \ldots a_0 a_n a_{n-1}}, A_n = \overline{a_{n-1} a_{n-2} \ldots a_1 a_0 a_n}$.