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Canadian Mathematical Olympiad - 2011 - Question 1

Source:

April 6, 2011
modular arithmeticnumber theory proposednumber theory

Problem Statement

Consider 7070-digit numbers with the property that each of the digits 1,2,3,...,71,2,3,...,7 appear 1010 times in the decimal expansion of nn (and 8,9,08,9,0 do not appear). Show that no number of this form can divide another number of this form.
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