Ibero American 2012 - Problem 6
Source:
October 3, 2012
logarithmsfloor functionnumber theory proposednumber theory
Problem Statement
Show that, for every positive integer , there exist consecutive positive integers such that none is divisible by the sum of its digits.(Alternative Formulation: Call a number good if it's not divisible by the sum of its digits. Show that for every positive integer there are consecutive good numbers.)