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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 aa and bb which have the same sum of their digits. For instance, 20122012 is shiny, because 2012=2005+72012 = 2005 + 7, and both 20052005 and 77 have the same sum of their digits. Find all positive integers which are not shiny (the dark integers).