MathDB

Partition M_k into two subsets

Source: IMO LongList 1988, Cuba 1, Problem 5 of ILL

October 22, 2005

combinatorics unsolvedcombinatorics

Problem Statement

Let

k

be a positive integer and

M_k

the set of all the integers that are between

2 \cdot k^2 + k

and

2 \cdot k^2 + 3 \cdot k,

both included. Is it possible to partition

M_k

into 2 subsets

A

and

B

such that

\sum_{x \in A} x^2 = \sum_{x \in B} x^2.