MathDB

36

Part of 1974 IMO Longlists

Problems(1)

All binomials are even [ILL 1974]

Source:

1/3/2011
Consider the binomial coefficients (nk)=n!k!(n−k)! (k=1,2,…n−1)\binom{n}{k}=\frac{n!}{k!(n-k)!}\ (k=1,2,\ldots n-1). Determine all positive integers nn for which (n1),(n2),…,(nn−1)\binom{n}{1},\binom{n}{2},\ldots ,\binom{n}{n-1} are all even numbers.
ARMLbinomial coefficients