MathDB

5

Part of 1997 ITAMO

Problems(1)

gcd of set of permutation of the digits of n

Source: 1997 ITAMO p5

1/25/2020
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.
number theorygreatest common divisorpermutationsmaximum