MathDB

Given an integer

m > 1

, we call the number

x{}

dangerous if

x{}

divides the number

y{}

, which is obtained by writing the digits of

x{}

in base

m{}

in reverse order, with

x\neq y

. Prove that if there exists a three-digit (in base

m

) dangerous number for a given

m

, then there exists a two-digit (in base

m

) dangerous number.

Problem Statement