MathDB

1

Part of 2000 Iran MO (2nd round)

Problems(2)

Dividing the set of positive integers into three subsets

Source:

10/15/2010
Find all positive integers nn such that we can divide the set {1,2,3,…,n}\{1,2,3,\ldots,n\} into three sets with the same sum of members.
number theory proposednumber theoryalgebraset theorySubsets
an interesting set

Source:

3/11/2005
2121 distinct numbers are chosen from the set {1,2,3,…,2046}.\{1,2,3,\ldots,2046\}. Prove that we can choose three distinct numbers a,b,ca,b,c among those 2121 numbers such that bc<2a2<4bcbc<2a^2<4bc
combinatorics