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Number of ways to express n as sum of distinct numbers

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September 2, 2010
functionnumber theoryAdditive Number TheoryAdditive combinatoricscountingIMO ShortlistIMO Longlist

Problem Statement

Let nn be a positive integer. Prove that the number of ways to express nn as a sum of distinct positive integers (up to order) and the number of ways to express nn as a sum of odd positive integers (up to order) are the same.
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