MathDB

partition of a set

Source:

November 25, 2005

quadraticspigeonhole principlecombinatorics proposedcombinatorics

Problem Statement

Given positive integers

n_1<n_2<...<n_{2000}<10^{100}

. Prove that we can choose from the set

\{n_1,...,n_{2000}\}

nonempty, disjont sets

A

and

B

which have the same number of elements, the same sum and the same sum of squares.