MathDB

Least k for which there exist x,y,z

Source: 2012cmo,problem6

January 12, 2012

modular arithmeticpigeonhole principleinequalitiescombinatorics proposedcombinatorics

Problem Statement

Find the smallest positive integer

k

such that, for any subset

A

S=\{1,2,\ldots,2012\}

with

|A|=k

, there exist three elements

x,y,z

A

such that

x=a+b

y=b+c

z=c+a

, where

a,b,c

are in

S

and are distinct integers.
Proposed by Huawei Zhu