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1990, 1990 + 1, 1990 + 2, ..., 1990 + k

Source: IMO ShortList 1990, Problem 15 (MEX 2)

August 15, 2008

inductioncombinatoricspartitionSet systemsIMO Shortlist

Problem Statement

Determine for which positive integers

k

the set X \equal{} \{1990, 1990 \plus{} 1, 1990 \plus{} 2, \ldots, 1990 \plus{} k\} can be partitioned into two disjoint subsets

A

and

B

such that the sum of the elements of

A

is equal to the sum of the elements of

B.