Partitioning integers from 1 to 999999
Source: All-Russian MO 2001 Grade 9 #1; Grade 10 #1
January 2, 2012
ceiling functionfloor functionnumber theory unsolvednumber theory
Problem Statement
The integers from to are partitioned into two groups: the first group consists of those integers for which the closest perfect square is odd, whereas the second group consists of those for which the closest perfect square is even. In which group is the sum of the elements greater?