MathDB
Ibero American 2012 - Problem 6

Source:

October 3, 2012
logarithmsfloor functionnumber theory proposednumber theory

Problem Statement

Show that, for every positive integer nn, there exist nn 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 nn there are nn consecutive good numbers.)