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TH-TMO 2007 Problem 14

    The sum ∑k=848000(k84)(8084−k84)\sum_{k=84}^{8000}{k \choose 84}{{8084 - k} \choose 84} can be written as a binomial coefficient (ab)a \choose b for integers a,ba, b . Find a possible pair (a,b)(a, b)

    Dataset text AI-MO AoPS. Quoted with source.

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