15

Part of 1990 IMO Shortlist

Problems(1)

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

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

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

B

such that the sum of the elements of

A

is equal to the sum of the elements of

B.

inductioncombinatoricspartitionSet systemsIMO Shortlist