MathDB

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}

2