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.
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
1 Jan 2001