Ibero American 2012 - Problem 2
Source: Ibero American 2012
October 2, 2012
number theory proposednumber theory
Problem Statement
A positive integer is called shiny if it can be written as the sum of two not necessarily distinct integers and which have the same sum of their digits. For instance, is shiny, because , and both and have the same sum of their digits. Find all positive integers which are not shiny (the dark integers).