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Turkey NMO 2001 Problem 3

Source: Turkey NMO 2001 Problem 3

September 30, 2011
combinatorics proposedcombinatorics

Problem Statement

One wants to distribute nn same sized cakes between kk people equally by cutting every cake at most once. If the number of positive divisors of nn is denoted as d(n)d(n), show that the number of different values of kk which makes such distribution possible is n+d(n)n+d(n)
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