MathDB

12

Part of 1982 IMO Longlists

Problems(1)

Prove that there are exactly 1982 numbers

Source: IMO LongList 1982 - P12

3/16/2011
Let there be 33993399 numbers arbitrarily chosen among the first 67986798 integers 1,2,…,67981, 2, \ldots , 6798 in such a way that none of them divides another. Prove that there are exactly 19821982 numbers in {1,2,…,6798}\{1, 2, \ldots, 6798\} that must end up being chosen.
combinatorics unsolvedcombinatorics