Exploring 2016 Usamo Problem 5

Exploring 2016 Usamo Problem 5 reveals several interesting facts.

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More Olympiad geometry. Here, we have an equilateral pentagon AMNPQ inscribed in triangle ABC…and we want to prove that ... You can learn more about online Olympiad courses by visiting at https://www.momentumlearning.org and click on the "online" tab ... You can learn more about online Olympiad courses by visiting at https://www.momentumlearning.org and click on the "online" tab ... IMO

What are the only positive integers 'k' for which the average of the k-th powers of the binomial coefficients is always an integer?

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