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3-stratum numbers - Iran NMO 2003 (Second Round) - Problem1

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October 4, 2010
number theory proposednumber theory

Problem Statement

We call the positive integer nn a 3−3-stratum number if we can divide the set of its positive divisors into 33 subsets such that the sum of each subset is equal to the others. a)a) Find a 3−3-stratum number. b)b) Prove that there are infinitely many 3−3-stratum numbers.
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