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Each multiple k,2k,...,nk contains all the digits 0,1,..,9

Source: XVIII Cono Sur Mathematical Olympiad (2007)

August 10, 2011
number theory unsolvednumber theory

Problem Statement

Show that for each positive integer nn, there is a positive integer kk such that the decimal representation of each of the numbers k,2k,…,nkk, 2k,\ldots, nk contains all of the digits 0,1,2,…,90, 1, 2,\ldots, 9.
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