MathDB

7

Part of 1984 IMO Longlists

Problems(1)

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

Source:

10/12/2010
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.
number theoryleast common multiplefloor functionnumber theory unsolved