6

Part of 1986 Czech And Slovak Olympiad IIIA

Problems(1)

subset with any m,n satisfy |m-n| \ge mn/25

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1986 p6

M \subset N

has the property that every two numbers

m,n

M

|m-n| \ge mn/25

. Prove that the set

M

contains no more than

9

elements. Decide whether there exists such set M.

combinatoricsSubsetsinequalities