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MathNet 2010 — Part 02 Question 186

Math Olympiad Vault · MathNet 2010 — Part 02

Question 186

Let $I_{n}$ be the set of the first odd natural numbers $n$. For example: $I_{3} = \{1, 3, 5\}$, $I_{6} = \{1, 3, 5, 7, 9, 11\}$, etc. For which numbers $n$ the set $I_{n}$ can be decomposed into two (disjoint) parts so that the sums of the numbers in each of them coincide?