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Unformatted text preview: Divisibility of the middle binomial coeﬃcent
2n! The middle binomial coeﬃcient C(2n, n) = n!n! tends to be very composite. For example, it is always an even number. However, show that there are inﬁnitely many values of n such that: (a) (easy) C(2n, n) is not divisible by 3; (b) (diﬃcult) C(2n, n) is not divisible by 3 or 5; (c) (famous unsolved problem of mine worth $1000) C(2n, n) is not divisible by 3 or 5 or 7. 1 ...
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 Fall '07
 Graham

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