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C^{2n}_{n} divides lcm(1, 2, ..., 2n)

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October 12, 2010
number theoryleast common multiplefloor functionnumber theory unsolved

Problem Statement

Prove that for any natural number nn, the number (2nn)\dbinom{2n}{n} divides the least common multiple of the numbers 1,2,⋯ ,2n−1,2n1, 2,\cdots, 2n -1, 2n.
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