61st Putnam 2000

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Problem B2

m and n are positive integers with m ≤ n. d is their greatest common divisor. nCm is the binomial coefficient. Show that d/n nCm is integral.

 

Solution

Recall that d is a linear combination of m and n. n/n nCm is obviously integral, whilst m/n nCm = (n-1)C(m-1), which is also integral.

 


 

61st Putnam 2000

© John Scholes
jscholes@kalva.demon.co.uk
1 Jan 2001