Eötvös 1934/1 solution

Problem 1

E is the product 2·4·6 ... 2n, and D is the product 1·3·5 ... (2n-1). Show that, for some m, D·2^m is a multiple of E.

Solution

We have D = (2n)!/(2ⁿ n!), so 2²ⁿD/E = 2nCn, which is an integer.