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gcd of set of permutation of the digits of n

Source: 1997 ITAMO p5

January 25, 2020
number theorygreatest common divisorpermutationsmaximum

Problem Statement

Let XX be the set of natural numbers whose all digits in the decimal representation are different. For n∈Nn \in N, denote by AnA_n the set of numbers whose digits are a permutation of the digits of nn, and dnd_n be the greatest common divisor of the numbers in AnA_n. (For example, A1120={112,121,...,2101,2110}A_{1120} =\{112,121,...,2101,2110\}, so d1120=1d_{1120} = 1.) Find the maximum possible value of dnd_n.
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